Inverse trigonometric functions differentiation Calculator

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Example

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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

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

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

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

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