To determine

To find:

h' in terms of f' and g'

Answer

h'x=4.f'gsin⁡4x.g'sin4xcos⁡4x

Explanation

Differentiate by using differentiation rules

1) Formula:

(i) Chain rule:

ddxfgx=f'gxg'(x)

(ii) Constant multiple rule:

ddxC.fx=C.ddxfx

where C is constant.

2) Given:

hx=f(gsin⁡4x)

3) Calculation:

h'(x)=ddxf(gsin⁡4x)

By using chain rule,

ddxf(gsin⁡4x)=f'gsin⁡4x.g'sin⁡4x

Again by using chain rule,

ddxfgsin⁡4x=f'gsin⁡4x.g'sin4x.ddxsin⁡4x

By using constant multiple rule,

ddxfgsin⁡4x=4.f'gsin⁡4x.g'sin4xcos⁡4x

Conclusion:

h'x=4.f'gsin⁡4x.g'sin4xcos⁡4x