Calculus Examples

$\int_{6}^{x^{3}} \frac{1}{p^{2}} d p$

Step 1

Take the derivative of $\int_{6}^{x^{3}} \frac{1}{p^{2}} d p$ with respect to $x$ using Fundamental Theorem of Calculus and the chain rule.

$\frac{d}{d x} [x^{3}] \frac{1}{{(x^{3})}^{2}}$

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 $n = 3$ .

$3 x^{2} \frac{1}{{(x^{3})}^{2}}$

Step 2.2

Simplify terms.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

$3 x^{2} \frac{1}{x^{3 \cdot 2}}$

Step 2.2.1.2

Multiply $3$ by $2$ .

$3 x^{2} \frac{1}{x^{6}}$

Step 2.2.2

Combine $3$ and $\frac{1}{x^{6}}$ .

$x^{2} \frac{3}{x^{6}}$

Step 2.2.3

Combine $x^{2}$ and $\frac{3}{x^{6}}$ .

$\frac{x^{2} \cdot 3}{x^{6}}$

Step 2.2.4

Move $3$ to the left of $x^{2}$ .

$\frac{3 \cdot x^{2}}{x^{6}}$

Step 2.2.5

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Tap for more steps...

Step 2.2.5.1

Factor $x^{2}$ out of $3 x^{2}$ .

$\frac{x^{2} \cdot 3}{x^{6}}$

Step 2.2.5.2

Cancel the common factors.

Tap for more steps...

Step 2.2.5.2.1

Factor $x^{2}$ out of $x^{6}$ .

$\frac{x^{2} \cdot 3}{x^{2} x^{4}}$

Step 2.2.5.2.2

Cancel the common factor.

$\frac{x^{2} \cdot 3}{x^{2} x^{4}}$

Step 2.2.5.2.3

Rewrite the expression.

$\frac{3}{x^{4}}$