How do you differentiate $f(x)=sin^-1(x^3)$ ?

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Answer 1 · 2017-02-05T09:01:07

The answer is $=(3x^2)/(sqrt(1-x^6))$

Let $y=sin^-1x^3$

So,

$siny=x^3$

Differentiating wrt $x$

$cosy(dy/dx)=3x^2$

$dy/dx=(3x^2)/(cosy)$

But,

$sin^2y+cos^2y=1$

$cos^2y=1-sin^2y=1-x^6$

$cosy=sqrt(1-x^6)$

Therefore,

$dy/dx=f'(x)=(3x^2)/(sqrt(1-x^6))$

How do you differentiate f(x)=sin^-1(x^3)f(x)=sin^-1(x^3)?