How do you differentiate $f (x) = 3 arcsin (x^4)$ ?

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Answer 1 · 2018-03-31T15:17:01

$dy/dx=(12x^3)/sqrt(1-x^8)$

$f(x)=3arcsin(x^4)$

Let
$y=f(x)$

$3arcsin(x^4)=3sin^-1(x^4)$

$y=3sin^-1(x^4)$

Let $u=x^4$

$y=3sin^-1u$

$dy/dx=dy/(du).(du)/dx$

$y=3sin^-1u$

$dy/(du)=3xx1/sqrt(1-u^2)$

$u=x^4$

$u^2=(x^4)^2$
$u^2=x^8$

$dy/(du)=3/sqrt(1-x^8)$

$u=x^4$

$(du)/dx=4x^3$

$dy/dx=dy/(du).(du)/dx$

$dy/dx=(3/sqrt(1-x^8)).(4x^3)$

$dy/dx=(12x^3)/sqrt(1-x^8)$

How do you differentiate f (x) = 3 arcsin (x^4)f (x) = 3 arcsin (x^4)?