Calculus Examples

$\int_{0}^{x^{3}} e^{- 4 t} d t$

Step 1

Take the derivative of $\int_{0}^{x^{3}} e^{- 4 t} d t$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [x^{3}] e^{- 4 x^{3}}$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$3 x^{2} e^{- 4 x^{3}}$