Calculus Examples

$x^{2} \sin (y)$

Step 1

Since $\sin (y)$ is constant with respect to $x$ , the derivative of $x^{2} \sin (y)$ with respect to $x$ is $\sin (y) \frac{d}{d x} [x^{2}]$ .

$\sin (y) \frac{d}{d x} [x^{2}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$\sin (y) (2 x)$

Step 3

Reorder.

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Step 3.1

Move $2$ to the left of $\sin (y)$ .

$2 \cdot \sin (y) x$

Step 3.2

Reorder the factors of $2 \sin (y) x$ .

$2 x \sin (y)$