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

1 Answer
Bdub
Apr 14, 2016

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

Explanation:

#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)#

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