Derivatives of exponential functions practice problems
eˣ and its relatives, usually with the chain rule close behind. 52 problems with worked solutions; in 52 of them every equation is proved by a computer algebra system.
Differentiate \( \displaystyle f(x) = - e^{x} \).
Differentiate \( \displaystyle f(x) = e^{x - 1} \).
Differentiate \( \displaystyle f(x) = e^{3 x + 5} \).
Differentiate \( \displaystyle f(x) = e^{3 x - 3} \).
Differentiate \( \displaystyle f(x) = 2 e^{x} \).
Differentiate \( \displaystyle f(x) = \frac{e^{3 x - 3}}{3} \).
Differentiate \( \displaystyle f(x) = 5 e^{x + 1} \).
Differentiate \( \displaystyle f(x) = \frac{e^{4 x + 1}}{4} \).
Differentiate \( \displaystyle f(x) = - e^{x - 1} \).
Differentiate \( \displaystyle f(x) = e^{3 x - 7} \).
Differentiate \( \displaystyle f(x) = e^{6 x + 8} \).
Differentiate \( \displaystyle f(x) = e^{x - 3} \).
Differentiate \( \displaystyle f(x) = \frac{e^{5 x + 1}}{5} \).
Differentiate \( \displaystyle f(x) = \left(x - 1\right) e^{x} \).
Differentiate \( \displaystyle f(x) = 2 \left(x - 1\right) e^{x} \).
Differentiate \( \displaystyle f(x) = 5 \left(x - 1\right) e^{x} \).
Differentiate \( \displaystyle f(x) = 2 x e^{4 x} \).
Differentiate \( \displaystyle f(x) = \left(4 x + 2\right) e^{8 x + 4} \).
Differentiate \( \displaystyle f(x) = - \frac{e^{2 x + 1}}{2} \).
Differentiate \( \displaystyle f(x) = x e^{2 x} \).
Differentiate \( \displaystyle f(x) = \left(2 x - 3\right) e^{4 x - 6} \).
Differentiate \( \displaystyle f(x) = \frac{2 e^{3 x - 1}}{3} \).
Differentiate \( \displaystyle f(x) = \left(3 x - 3\right) e^{6 x - 6} \).
Differentiate \( \displaystyle f(x) = \frac{3 e^{2 x + 1}}{2} \).
Differentiate \( \displaystyle f(x) = - \frac{e^{4 x + 2}}{4} \).
Differentiate \( \displaystyle f(x) = \frac{2 e^{5 x + 1}}{5} \).
Differentiate \( \displaystyle f(x) = - \frac{e^{4 x - 1}}{4} \).
Differentiate \( \displaystyle f(x) = x^{2} + e^{x} + 4 \).
Differentiate \( \displaystyle f(x) = e^{4 x^{2} + 1} \).
Differentiate \( \displaystyle f(x) = e^{\cos{\left(2 x - 1 \right)}} \).
Differentiate \( \displaystyle f(x) = \frac{e^{x - 1}}{x} \).
Differentiate \( \displaystyle f(x) = e^{- x} \sin{\left(x \right)} \).
Differentiate \( \displaystyle f(x) = \sqrt{x - 3} e^{x - 3} \).
Differentiate \( \displaystyle f(x) = e^{- 3 x} \sin{\left(3 x \right)} \).
Differentiate \( \displaystyle f(x) = e^{x} \ln{\left(x \right)} \).
Differentiate \( \displaystyle f(x) = \sqrt{x - 1} e^{x - 1} \).
Differentiate \( \displaystyle f(x) = \left(x + 2\right)^{2} e^{- x - 2} \).
Differentiate \( \displaystyle f(x) = \sqrt{x} e^{x} \).
Differentiate \( \displaystyle f(x) = e^{\left(5 x + 2\right)^{2} + 1} \).
Differentiate \( \displaystyle f(x) = e^{x^{2} + 1} \).
Differentiate \( \displaystyle f(x) = e^{9 x^{2} + 1} \).
Differentiate \( \displaystyle f(x) = \frac{e^{3 x + 1}}{3 x + 2} \).
Differentiate \( \displaystyle f(x) = \frac{e^{5 x}}{5 x + 1} \).
Differentiate \( \displaystyle f(x) = e^{\cos{\left(2 x \right)}} \).
Differentiate \( \displaystyle f(x) = \sqrt{5} \sqrt{x} e^{5 x} \).
Differentiate \( \displaystyle f(x) = \sqrt{2} \sqrt{x} e^{2 x} \).
Differentiate \( \displaystyle f(x) = e^{- 2 x} \sin{\left(2 x \right)} \).
Differentiate \( \displaystyle f(x) = \left(2 x - 1\right)^{2} e^{1 - 2 x} \).
Differentiate \( \displaystyle f(x) = e^{\left(2 x - 1\right)^{2} + 1} \).
Differentiate \( \displaystyle f(x) = e^{3 - x} \sin{\left(x - 3 \right)} \).
Differentiate \( \displaystyle f(x) = \frac{e^{4 x}}{4 x + 1} \).
Differentiate \( \displaystyle f(x) = e^{\cos{\left(x \right)}} \).