Calculus Examples

$y = 5 x^{2} e^{3} x$

Step 1

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [5 (x^{1} x^{2}) e^{3}]$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [5 x^{1 + 2} e^{3}]$

Step 3

Add $1$ and $2$ .

$\frac{d}{d x} [5 x^{3} e^{3}]$

Step 4

Since $5 e^{3}$ is constant with respect to $x$ , the derivative of $5 x^{3} e^{3}$ with respect to $x$ is $5 e^{3} \frac{d}{d x} [x^{3}]$ .

$5 e^{3} \frac{d}{d x} [x^{3}]$

Step 5

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$5 e^{3} (3 x^{2})$

Step 6

Multiply $3$ by $5$ .

$15 e^{3} x^{2}$