Calculus Examples

$x^{- 2} + 5 x^{2} y = x^{6}$

Step 1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 6$ .

$f' (x) = 6 x^{5}$

Step 2

Find the second derivative.

Tap for more steps...

Step 2.1

Since $6$ is constant with respect to $x$ , the derivative of $6 x^{5}$ with respect to $x$ is $6 \frac{d}{d x} [x^{5}]$ .

$6 \frac{d}{d x} [x^{5}]$

Step 2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 5$ .

$6 (5 x^{4})$

Step 2.3

Multiply $5$ by $6$ .

$f'' (x) = 30 x^{4}$