Calculus Examples

$\arcsin (x) + \arccos (x)$

Step 1

By the Sum Rule, the derivative of $\arcsin (x) + \arccos (x)$ with respect to $x$ is $\frac{d}{d x} [\arcsin (x)] + \frac{d}{d x} [\arccos (x)]$ .

$\frac{d}{d x} [\arcsin (x)] + \frac{d}{d x} [\arccos (x)]$

Step 2

The derivative of $\arcsin (x)$ with respect to $x$ is $\frac{1}{\sqrt{1 - x^{2}}}$ .

$\frac{1}{\sqrt{1 - x^{2}}} + \frac{d}{d x} [\arccos (x)]$

Step 3

The derivative of $\arccos (x)$ with respect to $x$ is $- \frac{1}{\sqrt{1 - x^{2}}}$ .

$\frac{1}{\sqrt{1 - x^{2}}} - \frac{1}{\sqrt{1 - x^{2}}}$

Step 4

Subtract $\frac{1}{\sqrt{1 - x^{2}}}$ from $\frac{1}{\sqrt{1 - x^{2}}}$ .

$0$