Q. 39 - Calculus

Question

Combining derivatives and integrals: Simplify each of the following as much as possible. 

$\frac{d}{dx}\int x^{3}dx$

Step-by-Step Solution

Answer

$\frac{d}{dx}\int x^{3}dx=x^3$

Step 1. Given information.

Given expression is $\frac{d}{dx}\int x^{3}dx$

We have to simply solve the expression.

Step 2. Solve the expression.

Now, $F\left(x\right)=\int f\left(x\right)$

So $\begin{array}{r}\frac{d}{dx}\int f\left(x\right)dx\\ =\frac{d}{dx}F\left(x\right)\\ =f\left(x\right)\end{array}$

Hence,

$\begin{array}{r}\frac{d}{d{x}^2}\int x^{3}dx\\ =x^3\end{array}$