Inverse trigonometric functions differentiation Calculator

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Example

Solved Problems

Difficult Problems

Solved example of inverse trigonometric functions differentiation

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

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 $4^2$

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

Multiply $-1$ times $16$

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

Applying the power of a power property

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

The derivative of a function multiplied by a constant ($4$) is equal to the constant times the derivative of the function

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

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

Subtract the values $2$ and $-1$

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

Multiply $4$ times $2$

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

Any expression to the power of $1$ is equal to that same expression

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

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

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

Final Answer

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

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!

Example

Solved Problems

Difficult Problems

Final Answer

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