From definition ,find derivatives of [tex]a^{x}[/tex]

Answers

Answer 1

Answer:

Step-by-step explanation:

d /d x [ a ^x ]

= d/ d x [ e ^ln ( a ) x ]

= e ^ln ( a ) x ⋅ d /d x [ ln ( a ) x ]

= e ^ln ( a ) x ⋅ ln ( a ) ⋅ d /d x [ x]

= e ^ln (a ) x ln ( a ) ⋅ 1

= ln ( a ) e ^ln ( a ) x

Rewrite/simplify:

= a ^x ln ( a )


Related Questions

What is the value of d that makes lines e and f parallel?
D=
10
13
85
115

Answers

Answer:

d = 13

Step-by-step explanation:

For the lines to be parallel, then

5(2d - 3) and (6d + 11 + 2d) will be corresponding angles and congruent, thus

5(2d - 3) = 6d + 11 + 2d ← distribute left side

10d - 15 = 8d + 11 ( subtract 8d from both sides )

2d - 15 = 11 ( add 15 to both sides )

2d = 26 ( divide both sides by 2 )

d = 13

The value of d that makes lines e and f parallel is 13units.

It is required to find the value of d.

What is line?

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

Given:

For the lines to be parallel, then

5(2d - 3) and (6d + 11 + 2d) will be corresponding angles and congruent.

According to given question we have,

5(2d - 3) = 6d + 11 + 2d

Distribute left side we get,

10d - 15 = 8d + 11  

subtract 8d from both sides we get,

2d - 15 = 11  

Add 15 to both sides  we get,

2d = 26

Divide both sides by 2 we get,

d = 13units.

Therefore, the value of d that makes lines e and f parallel is 13units.

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Find the value of x
3x + 40
5x - 45

Answers

3x + 40 = 5x - 45

2x = 85

x = 42.5

Answer:

<HOPE IT WILL HELP YOU >

Step-by-step explanation:

3x + 40

3x+40=0

3x= -- 40

x= -- 40/3

5x--45

5x--45=0

5x= 45

x =45/5

x = 9

Surveyors wished to know the distance across a lake between A and B. They measured the distance from B to C as 100 m and the angle from C to A to be 55°. Knowing that the angle between CB and BA was 90°, they used trig to solve for the distance. Show how it was done

Answers

Answer:

AB ≈ 70m

Step-by-step explanation:

Check the attachment for the diagram.

You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;

tan 35° = opposite/adjacent

tan 35° = AB/BC

tan 35° = AB/100

AB = 100tan35°

AB = 100 * 0.7002

AB = 70.02m

Hence the distance across a lake between A and B is approximately 70m

PLEASE ANSWER ASAP !!!!

Answers

At h=1 y=-2 so -2 hope it helps!

Which of the following statements BEST proves that ∠XWY ≌ ∠ZYW?

A.
If two parallel lines are cut by a transversal, then corresponding angles are congruent.

B.
If two parallel lines are cut by a transversal, then complementary angles are congruent.

C.
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

D.
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

Answers

Answer: C

Step-by-step explanation:

The pair of angles created on the inner side of the parallel lines intersected by a transversal but on opposing sides of the transversal is known as an alternative interior angle. The correct option is C.

What are Alternate Interior angles?

When two parallel lines are intersected by a transversal, the pair of angles created on the inner side of the parallel lines but on opposing sides of the transversal is known as an alternative interior angle. These angles are always equal in measure.

The best statements BEST that proves ∠XWY ≌ ∠ZYW is that If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

Hence, the correct option is C.

The complete question is mentioned in the image below.

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5/6 - 1/3 divided by 5/12

Answers

Answer:

1/30

Step-by-step explanation:

1-Intercambiamos los numeros de la ultima fraccion:

5/6 - 1/3 entre 5/12

2-intercambiamos posision, numeros y cambiamos el signo de resta a signo de multiplicacion:

1/3 x  12/5: 4/5

3-convertimos la operación en enteros (despues de aver hecho mas pasos)

25-24/30

4-restamos: 25 - 24=1

1/30

que espero te haya ser de mucha ayuda!!!

Find the value of x.
Area of rectangle = 36
▅ х
x + 5

Answers

The value of x is 4, which is determined by the quadratic equation.

What is the area of the rectangle?

The area of a rectangle is defined as the product of the length and width.

The rectangle of a rectangle = L × W

Where W is the width of the rectangle  and L is the length of the rectangle

We have been given that area of the rectangle = 36

Area of rectangle = width of the rectangle × length of the rectangle

Here the width of the rectangle = x

And length of the rectangle = x + 5

The rectangle of a rectangle = x × (x + 5)

36 = x² + 5x

x² + 5x - 36 = 0

x² + 9x - 4x - 36 = 0

(x + 9)(x - 4) = 0

x = -9 and x = 4

Take the value of x = 4 and the negative value is neglected because the dimension can't be negative.

Therefore, the value of x is 4.

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Question 5 of 5
Evaluate -(5-4)(52)
A.-1/25
B. 25
C. -25
D. 1/25

Answers

Answer:

it should be negative 52 so i would go with C

Step-by-step explanation: it is the closest to the answer

Evaluate -2x^2 2y, if x = -3 and y = -1.

Answers

ANSWER is 16.

look at the photo to see the step by step equation :)

Fully simplify the expression-3xy/6x

Answers

Answer:

-1xy

-------

2x

Step-by-step explanation:

divide all by 3

Answer:

−1/2x^2y

Step-by-step explanation:

If the sales tax rate is 7% in New York, then how much sales tax would you pay in New York for a $34 pair of
pants?

Please I need help fast

Answers

Answer:

you would pay 2.38 sales tax for a 34 dollar pair of pants

Step-by-step explanation:

Which equation represents the line that passes through the points (–4, 3) and (2, –12)?

–9x + 2y = 42

x + 2y = 2

5x + 2y = –14

2x + 5y = 7

Answers

Answer:

5x + 2y = –14

Step-by-step explanation:

Graph the points and find the equation from there.

Answer:

the answer is 5x + 2y = –14 their right

Step-by-step explanation:

HAVING BAD DAY HELP

Suppose Karen reads 50 pages per day during the week, but then reads 1.5 times as many pages on Saturday and Sunday. How many pages total will Karen read on Saturday and Sunday?

Answers

Answer:

150 total pages read over the weekend, 75 for Saturday and 75 for Sunday.

Step-by-step explanation:

50×1.5=75

75+75=150

Answer:

Step-by-step explanation:

50 pages, 1.5 times as many

multiply:

50 x 1.5 = 75

If by "1.5 times as many on satuday and sunday" is including both days and not separately it will be 75 pages on saturday and sunday together..

If it says that she read 1.5 times as many on Saturday and 1.5 times as many on sunday, It will be 75 on saturday and 75 on sunday which is 150 pages.

I hope this wasn't confusing, I'm not sure on the wording of the question a bit, but I gave both possible answers.

Please HELPPP 9 mins left!!!

Answers

Answer: 8°

Step-by-step explanation:

57+90=147

147+4x+1= 180

147+1= 148

148+4x=180

180-148=32

32/4=8

x=8°

Simplify the following to an expression involving a single
trig function with no fractions.

Answers

Answer    

Step-by-step explanation:

cos x

Herky is putting money into a savings account on a weekly basis to buy a DVD player that costs $179.40 including tax. He asks Mario how much he should save per week to buy the player in 8 weeks if he already has $35.00 saved. Mario gives him the answer and explains how he found the answer. What does Mario say?
He tells Herky he needs to save $18.05 per week. He explains that he found his answer by subtracting $35.00 from $179.40, then dividing the result by 8.
He tells Herky he needs to save $22.43 per week. He explains that he found his answer by dividing $179.40 by 8.
He tells Herky he needs to save $26.80 per week. He explains that he found his answer by adding $35.00 to $179.40, then dividing the result by 8.
He tells Herky he needs to save $57.43 per week. He explains that he found his answer by dividing $179.40 by 8, then adding $35.00.

Answers

Answer:

b

Step-by-step explanation:

can someone help with that?

if x+y=2, calculate:
P=4x (x-3)+4y(y-3)+8xy​

Answers

Answer:

Step-by-step explanation:

P = 4x(x - 3) + 4y(y - 3) + 8xy

  = 4x² - 12x + 4y² - 12y + 8xy

  = (4x² + 8xy + 4y²) - (12x + 12y)

 = 4(x² + 2xy + y²) - 12(x + y)

 = 4(x + y)² - 12(x + y)

x+y =2 ⇒ P = 4.2² - 12.2 = 16 - 24 = -8

4. What is the sum of trigonometric ratios Cos 16 and Cos 747
A. 0.276
B. 0.961
0.1.237
D. 1.922

Answers

Answer:

I'm not completing sure (maybe a)

Step-by-step explanation:

Which of the following is a rational number?
v1, v2, v3, v5

Answers

Answer:

5

Step-by-step explanation:

Gina Needs To Pack 130 Pens, 50 Pencils And 20 Erasers Into Identical Gift Bags So That Each Item Is Equally Distributed Among The Gift Bags. (I) Find The Largest Number Of Gift Bags That Can Be Packed. (Ii) Find The Number Of Each Item In A Gift Bag.

Answers

Answer:

Step-by-step explanation:

I think the best way is to split up the erasers before you do anything. That would mean there were 20 gift bags in all

If you did that, then each gift bag would contain 2 pencils with 10 left over.

Further 130 pens would divide up into 6 pens in each gift bag with 10 pens left over.

x>-4
Examine the inequality and its graph.
6 5 4 -3 -2 -1 0 1 2
Which values are part of the solution set? Check all
that apply.
O x= 3
x= -5
OX=--
1
2
x= -4.5
x= -4

Answers

Answer:

A and C

Step-by-step explanation:

did assignment on edge

X+5x-3x-4 simplified?

Answers

Answer:

3x-4

How to find it:

x + 5x - 3x - 4

Add like terms

6x - 3x - 4

Add like terms

3x - 4

Answer:

3x-4

Step-by-step explanation:

Combine like terms, x + 5x gives you 6x but then subtract 3x and you have only 3x.

Keep 4 the same and your answer is 3x-4

Mark brainliest if possible!

Write the distance from the Sun to Mercury in scientific notation. Include units with your answer

Answers

Answer:

4.600 x 107 km (3.075 x 10-1 A.U.)

Step-by-step explanation:

3:4 is equivalent to ____:20.

Answers

Answer:

4 time 5 equals to 20

3 times 5 is 15

15:20 is the answer

Step-by-step explanation:

The answer is 15 because 20 divided by 5 is 4 so you should times 3 by 5! Lmk and I can explain it better

Please explain how you got the answer. Will mark Brainliest if correct.

A:-56
B:56
C:-48
D:48

Answers

Answer:

Hi there!

Your answer is:

A: -56

Step-by-step explanation:

-14=1/4 X

Solve for x!

Multiply both sides by the inverse of 1/4, which is 4! (1/4*4=1)

-14=1/4x

*4     *4

-56 = 1x

ALSO! Check your work!

-14= 1/4(-56) ??????

-14 = -14 YES

Your answer is A: -56

-14=1/4 X

Multiply both sides with the inverse of one over four (1/4*4=1)

-14=1/4x

*4     *4

-56 = 1x

helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

B

Step-by-step explanation:

Realised I could stilll answer so i did, from what I can tell its b

PLEASE ANSWER THE QUESTION CORRECTLY!!!!!!!!!!!!

Answers

Answer: -2,2

Step-by-step explanation:

Solve x2 = −169. Thank youuuuuuuuuuu

Answers

Answer:

x=-84.5

Step-by-step explanation:

In the figure, m∠2 = 70. Find the measure of each angle.

Answers

Answer:

35 is the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-     angle number 3 is 70

2-    angle number 5 is 110

3-    angle number 8 is 110

4-    angle number 1 is 110

5-    angle number 4 is 110

6-    anle number 6 is 70

Solve the inequality 2x + 10 < 5x + 1

Answers

Answer:

3 < x

Step-by-step explanation:

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