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# Inverse trigonometric functions differentiation Calculator

## Get detailed solutions to your math problems with our Inverse trigonometric functions differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of inverse trigonometric functions differentiation. This solution was automatically generated by our smart calculator:

$\frac{d}{dx}\left(\arcsin\left(4x^2\right)\right)$
2

Taking the derivative of arcsine

$\frac{1}{\sqrt{1-\left(4x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)$

The power of a product is equal to the product of it's factors raised to the same power

$\frac{1}{\sqrt{1-4^2\left(x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)$

Calculate the power $4^2$

$\frac{1}{\sqrt{1-16\left(x^2\right)^2}}\frac{d}{dx}\left(4x^2\right)$

Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$

$16x^{2\cdot 2}$

Multiply $2$ times $2$

$16x^{4}$

Multiply $2$ times $2$

$\frac{1}{\sqrt{1-16x^{4}}}\frac{d}{dx}\left(4x^2\right)$
3

The power of a product is equal to the product of it's factors raised to the same power

$\frac{1}{\sqrt{1- 16x^{4}}}\frac{d}{dx}\left(4x^2\right)$
4

Multiply $-1$ times $16$

$\frac{1}{\sqrt{1-16x^{4}}}\frac{d}{dx}\left(4x^2\right)$
5

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$4\left(\frac{1}{\sqrt{1-16x^{4}}}\right)\frac{d}{dx}\left(x^2\right)$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x^{\left(2-1\right)}$

Subtract the values $2$ and $-1$

$8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x$
6

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$4\cdot 2\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x$
7

Multiply $4$ times $2$

$8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x$

Multiply the fraction by the term

$\frac{8\cdot 1x}{\sqrt{1-16x^{4}}}$

Any expression multiplied by $1$ is equal to itself

$\frac{8x}{\sqrt{1-16x^{4}}}$
8

Multiply the fraction by the term

$\frac{8x}{\sqrt{1-16x^{4}}}$

##  Final answer to the problem

$\frac{8x}{\sqrt{1-16x^{4}}}$

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