Given y = f(u) and u = g(x), find dy/dx = f(g(x))g(x).
-$$y = \sin u , u = 7 x + 19$$
A) $\cos ( 7 x + 19 )$
B) $- 7 \cos ( 7 x + 19 )$
C) $7 \cos ( 7 x + 19 )$
D) $- \cos ( 7 x + 19 )$

Question

Quizplus · Accepted Answer

We have y = f(u) = sin u and u = g(x) = 7x + 19. Using the chain rule, we have:

dy/dx = dy/du * du/dx
dy/du = cos u (derivative of sin u)
du/dx = 7 (derivative of 7x + 19)

Therefore, dy/dx = cos u * 7 = cos(7x + 19) * 7 = 7cos(7x + 19). So the answer is C).

Given Y = F(u) and U = G(x), Find Dy/dx y=sin⁡u,u=7x+19y = \sin u , u = 7 x + 19y=sinu,u=7x+19

Given Y = F(u) and U = G(x), Find Dy/dx $y = \sin u , u = 7 x + 19$