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.
Includes
Standards
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)?
e^(2x+1)
2e^(2x+1)
(2x+1)e^(2x)
e^(2x+1)ln(2)
2. If f(x) = 3^(x^2), what is f'(x)?
x * 3^(x^2-1)
3^(x^2) * ln(3)
2x * 3^(x^2) * ln(3)
2x * 3^(x^2)
1. The derivative of e^x is always positive.
True
False
2. The derivative of y = 5^x is 5^x.
True
False
1. Find the derivative of y = x * e^x.
2. Find the derivative of y = e^(sin(x)).