Calculus Examples

$y = 2 \arcsin (x)$

Step 1

Set $y$ as a function of $x$ .

$f (x) = 2 \arcsin (x)$

Step 2

Find the derivative.

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Step 2.1

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

$2 \frac{d}{d x} [\arcsin (x)]$

Step 2.2

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

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

Step 2.3

Combine $2$ and $\frac{1}{\sqrt{1 - x^{2}}}$ .

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

Step 3

Set the derivative equal to $0$ then solve the equation $\frac{2}{\sqrt{1 - x^{2}}} = 0$ .

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Step 3.1

Set the numerator equal to zero.

$2 = 0$

Step 3.2

Since $2 \neq 0$ , there are no solutions.

No solution

Step 4

There are no solution found by setting the derivative equal to $0$ , $\frac{2}{\sqrt{1 - x^{2}}} = 0$ so there are no horizontal tangent lines.

No horizontal tangent lines found

Step 5