Calculus Examples

$\sin (x + y) = x y$

Step 1

Set $\sin (x + y)$ as a function of $x$ .

$f (x) = x y$

Step 2

Find the derivative.

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Step 2.1

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

$y \frac{d}{d x} [x]$

Step 2.2

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

$y \cdot 1$

Step 2.3

Multiply $y$ by $1$ .

$y$

Step 3

The roots of the derivative $y$ cannot be found.

No horizontal tangent lines.

Step 4