Calculus Examples

$x^{5} y^{3}$

Step 1

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

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

Step 2

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

$y^{3} (5 x^{4})$

Step 3

Reorder.

Tap for more steps...

Step 3.1

Move $5$ to the left of $y^{3}$ .

$5 \cdot y^{3} x^{4}$

Step 3.2

Reorder the factors of $5 y^{3} x^{4}$ .

$5 x^{4} y^{3}$