Calculus Examples

$\int_{1}^{x^{2}} \sqrt{3 + r^{3}} d r$

Step 1

Take the derivative of $\int_{1}^{x^{2}} \sqrt{3 + r^{3}} d r$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [x^{2}] \sqrt{3 + {(x^{2})}^{3}}$

Step 2

Differentiate using the Power Rule.

Tap for more steps...

Step 2.1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 x \sqrt{3 + {(x^{2})}^{3}}$

Step 2.2

Multiply the exponents in ${(x^{2})}^{3}$ .

Tap for more steps...

Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 x \sqrt{3 + x^{2 \cdot 3}}$

Step 2.2.2

Multiply $2$ by $3$ .

$2 x \sqrt{3 + x^{6}}$