Given y = f(u) and u = g(x), find dy/dx = f(g(x))g(x).
-$$y = u ^ { 2 } , u = 5 x - 1$$
A) 10x - 5
B) 50x
C) 25x - 5
D) 50x - 10

Question

Quizplus · Accepted Answer

Using the chain rule, we have

dy/dx = dy/du * du/dx
We can find dy/du by taking the derivative of y with respect to u, which is

dy/du = 2u

and we can find du/dx by taking the derivative of u with respect to x, which is

du/dx = 5

Substituting these back into the original formula, we get:

dy/dx = dy/du * du/dx = 2u * 5 = 10u

Now we substitute u = 5x - 1:

dy/dx = 10u = 10(5x - 1) = 50x - 10

Therefore, the answer is D: 50x - 10.

Given Y = F(u) and U = G(x), Find Dy/dx y=u2,u=5x−1y = u ^ { 2 } , u = 5 x - 1y=u2,u=5x−1