Calculus Examples

$y = x^{4} + 6 e^{x}$

Step 1

Differentiate.

Tap for more steps...

Step 1.1

By the Sum Rule, the derivative of $x^{4} + 6 e^{x}$ with respect to $x$ is $\frac{d}{d x} [x^{4}] + \frac{d}{d x} [6 e^{x}]$ .

$\frac{d}{d x} [x^{4}] + \frac{d}{d x} [6 e^{x}]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$4 x^{3} + \frac{d}{d x} [6 e^{x}]$

Step 2

Evaluate $\frac{d}{d x} [6 e^{x}]$ .

Tap for more steps...

Step 2.1

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

$4 x^{3} + 6 \frac{d}{d x} [e^{x}]$

Step 2.2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $e$ .

$4 x^{3} + 6 e^{x}$