Calculus Examples

$r = {(\frac{1 + \sin (x)}{1 - \cos (x)})}^{2}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d ?} (r) = \frac{d}{d ?} ({(\frac{1 + \sin (x)}{1 - \cos (x)})}^{2})$

Step 2

The derivative of $r$ with respect to $?$ is $r'$ .

$r'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Apply the product rule to $\frac{1 + \sin (x)}{1 - \cos (x)}$ .

$\frac{d}{d ?} [\frac{{(1 + \sin (x))}^{2}}{{(1 - \cos (x))}^{2}}]$

Step 3.2

Since $\frac{{(1 + \sin (x))}^{2}}{{(1 - \cos (x))}^{2}}$ is constant with respect to $?$ , the derivative of $\frac{{(1 + \sin (x))}^{2}}{{(1 - \cos (x))}^{2}}$ with respect to $?$ is $0$ .

$0$

Step 4

Reform the equation by setting the left side equal to the right side.

$r' = 0$

Step 5

Replace $r'$ with $\frac{d r}{d ?}$ .

$\frac{d r}{d ?} = 0$