How do you find the derivative of $f (x) = \sqrt{cos (e^{x^{4} sin (x)})}$ $f(x)=sqrt(cos(e^(x^4sin(x)))$ ?

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Answer 1 · 2016-04-14T20:03:08

$f'(x)==1/(2sqrt(cos(e^(x^4sinx))) )xx-sin(e^(x^4sinx))xx e^(x^4sinx)xx(x^4cosx+4x^3sinx)$

$f(x)=sqrtx, g(x)=cos x, h(x)=e^x, r(x)=x^4sinx$

$f(g(h(r(x))))=sqrt(cos(e^(x^4sinx))$

$[f(g(h(r(x))))]'=f'(g(h(r(x))))*g'(h(r(x))) h'(r(x))*r'(x)$

$=1/(2sqrt(cos(e^(x^4sinx))) )xx-sin(e^(x^4sinx))xx e^(x^4sinx)xx(x^4cosx+4x^3sinx)$

How do you find the derivative of f(x)=sqrt(cos(e^(x^4sin(x)))f(x)=√cos(ex4sin(x))f(x)=sqrt(cos(e^(x^4sin(x)))?