Calculus Examples

$e^{\ln (5 x^{10})}$

Step 1

Exponentiation and log are inverse functions.

$\frac{d}{d x} [5 x^{10}]$

Step 2

Since $5$ is constant with respect to $x$ , the derivative of $5 x^{10}$ with respect to $x$ is $5 \frac{d}{d x} [x^{10}]$ .

$5 \frac{d}{d x} [x^{10}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 10$ .

$5 (10 x^{9})$

Step 4

Multiply $10$ by $5$ .

$50 x^{9}$