How do you find the derivative of the function: $arcsin (x^{2})$ $arcsin(x^2)$ ?

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How do you find the derivative of the function: $arcsin (x^{2})$ $arcsin(x^2)$ ?

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Answer 1 · 2016-02-06T19:25:17

$\frac{2 x}{\sqrt{1 - x^{4}}}$ $( 2x)/(sqrt(1-x^4)$

Explanation:

$\frac{d}{d x} (arcsin x) = \frac{1}{\sqrt{1 - x^{2}}}$ $d/dx(arcsinx) = 1/sqrt(1-x^2)$

( this should be known as it is fairly standard )

for the question here the derivative is the same but $x = x^{2}$ $x = x^2$

differentiate using the $chain rule$ $color(blue)(" chain rule ")$

$\Rightarrow \frac{d}{d x} [arcsin (x^{2})] = \frac{1}{\sqrt{1 - x^{4}}} \frac{d}{d x} (x^{2})$ $rArr d/dx[arcsin(x^2)] = 1/sqrt(1- x^4) d/dx(x^2)$

$= \frac{2 x}{\sqrt{1 - x^{4}}}$ $= (2x)/sqrt(1-x^4)$

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How do you find the derivative of the function: $arcsin (x^{2})$ $arcsin(x^2)$ ?

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