Question

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

Answer 1

`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)`