Find dy/dx for the following functions

Question

Given y=f(u) and u=g(x), find dy/dx if f'(g(x)g'(x) for the following functions. y=sin u, u= 7x+3

Answer 1

Given y = f(u) and u = g(x),

that means that y = f(g(x)).

So the function y is the composition of the functions f and g.

Therefore, by the Chain Rule,

dy/dx = f'(g(x))g'(x).

Note that you forgot one of the parentheses in the expression f'(g(x))g'(x).

Given that y = f(u) = sin(u),

we have f'(u) = cos u.

Given that u = g(x) = 7x + 3,

we have g'(x) = 7.

Therefore dy/dx = f'(g(x))g'(x) = (cos (7x + 3))7

Let's write this more legibly as dy/dx = 7cos(7x + 3)

Thanks.