Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x.
-$$y = ( - 2 x + 11 ) ^ { 5 }$$
A) $y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = - 10 ( - 2 x + 11 ) ^ { 4 }$
B) $y = 5 u + 11 ; u = x ^ { 5 } ; \frac { d y } { d x } = - 10 x ^ { 4 }$
C) $y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = - 2 ( - 2 x + 11 ) ^ { 5 }$
D) $y = u ^ { 5 } ; u = - 2 x + 11 ; \frac { d y } { d x } = 5 ( - 2 x + 11 ) ^ { 4 }$

Question

Quizplus · Accepted Answer

We need to use the chain rule to find dy/dx. First, we identify the inner function as u(x) = -2x + 11 and the outer function as y(u) = u^5. Then, we apply the chain rule:

dy/dx = dy/du * du/dx

We know that dy/du = 5u^4, and du/dx = -2. Plugging in u(x) = -2x + 11, we get:

dy/dx = 5(-2x + 11)^4 * -2
dy/dx = -10(-2x + 11)^4

Therefore, the answer is A.

Write the Function in the Form Y = F(u) and U