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Inverse trigonometric functions differentiation Calculator

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1

Solved example of inverse trigonometric functions differentiation

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

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 $f'(x) = nx^{n-1}$

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

Subtract the values $2$ and $-1$

$8\left(\frac{1}{\sqrt{1-16x^{4}}}\right)x$
5

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

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

Multiply the fraction and term

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

Final Answer

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

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