Question

Find the nth derivative of sin^3 x

Answer 1

Left f(x) = x³ and g(x) = sin(x) 

Therefore your function written as a composition of functions is: 

f(g(x)) = sin³(x) 

Then the chain rule says that its derivative should be: 

f'(g(x))g'(x) 

Therefore, your answer is: 

dy/dx = 3sin²(x)cos(x)