To determine
To find:
h' in terms of f' and g'
Answer
h'x=4.f'gsin4x.g'sin4xcos4x
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(gsin4x)
3) Calculation:
h'(x)=ddxf(gsin4x)
By using chain rule,
ddxf(gsin4x)=f'gsin4x.g'sin4x
Again by using chain rule,
ddxfgsin4x=f'gsin4x.g'sin4x.ddxsin4x
By using constant multiple rule,
ddxfgsin4x=4.f'gsin4x.g'sin4xcos4x
Conclusion:
h'x=4.f'gsin4x.g'sin4xcos4x