Given y = f(u) and u = g(x), find dy/dx = f(g(x))g(x).
-$$y = u ( u - 1 ) , u = x ^ { 2 } + x$$
A) $4 x ^ { 3 } + 6 x ^ { 2 } - 2 x$
B) $4 x ^ { 3 } + 6 x ^ { 2 } - 1$
C) $2 x ^ { 2 } + 4 x + 1$
D) $2 x ^ { 2 } + 4 x$

Question

Quizplus · Accepted Answer

We have that:
$$u = x^2 + x$$
Therefore, 
$$f(u) = u(u-1) = (x^2 + x)(x^2 + x - 1)$$
Using the chain rule, we have:
$$y' = \frac{dy}{dx} = \frac{dy}{du}\cdot\frac{du}{dx} = f'(u)g'(x) = (2u-1)(2x+1)$$
Plugging in for u, we get:
$$y' = (2(x^2+x)-1)(2x+1) = (2x^2 + 4x - 1)(2x+1) = 4x^3 + 6x^2 - 1$$
Therefore, the correct answer is (B).

Given Y = F(u) and U = G(x), Find Dy/dx y=u(u−1),u=x2+xy = u ( u - 1 ) , u = x ^ { 2 } + xy=u(u−1),u=x2+x

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