How do you differentiate $y = arcsin (x^{2})$ $y=arcsin(x^2)$ ?

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How do you differentiate $y = arcsin (x^{2})$ $y=arcsin(x^2)$ ?

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Answer 1 · 2017-01-29T20:53:46

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

Explanation:

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

$color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(arcsin(f(x)))=1/(sqrt(1-f(x)^2)).f'(x))color(white)(2/2)|)))$

$y=arcsin(x^2)$

$rArrdy/dx=1/(sqrt(1-(x^2)^2)).d/dx(x^2)$

$=(2x)/(sqrt(1-x^4))$

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How do you differentiate $y = arcsin (x^{2})$ $y=arcsin(x^2)$ ?

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