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Derivatives of Exponential Functions

A Grade 12 Calculus worksheet covering the derivatives of exponential functions, including natural exponential functions and those with an arbitrary base.

Grade 12 Math CalculusDerivatives of Exponential Functions
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Includes

Fill in the Blanks2 Short AnswerMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.B.5CCSS.MATH.CONTENT.HSF.LE.A.4
7 sections · Free to use · Printable
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Derivatives of Exponential Functions

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Read each question carefully and show all your work. Simplify your answers where possible.

1. The derivative of e^x is  .

2. The derivative of a^x is  .

3. The derivative of e^(f(x)) is  .

1. Find the derivative of f(x) = 5e^x.

2. Find the derivative of g(x) = e^(3x).

3. Find the derivative of h(x) = 2^(x^2).

1. Which of the following is the derivative of y = e^(2x+1)?

a

e^(2x+1)

b

2e^(2x+1)

c

(2x+1)e^(2x)

d

e^(2x+1)ln(2)

2. If f(x) = 3^(x^2), what is f'(x)?

a

x * 3^(x^2-1)

b

3^(x^2) * ln(3)

c

2x * 3^(x^2) * ln(3)

d

2x * 3^(x^2)

1. The derivative of e^x is always positive.

T

True

F

False

2. The derivative of y = 5^x is 5^x.

T

True

F

False

1. Find the derivative of y = x * e^x.

2. Find the derivative of y = e^(sin(x)).