Find $d y / d u , d u / d x \text {, and } d y / d x$ of the functions $y = u ^ { 2 } , u = 4 x + 7$ .
A) $d y / d u = 2 u , d u / d x = 4 , \text { and } d y / d x = 32 x + 56$
B) $d y / d u = 2 u , d u / d x = 2 \text {, and } d y / d x = 16 x + 49$
C) $d y / d u = 4 u , d u / d x = 4 , \text { and } d y / d x = 32 x + 56$
D) $d y / d u = 4 u , d u / d x = 2 , \text { and } d y / d x = 32 x + 56$
E) $d y / d u = 2 u , d u / d x = 4 \text {, and } d y / d x = 16 x + 49$

Question

Quizplus · Accepted Answer

Given $y = u^2$ and $u = 4x + 7$, the derivative of $y$ with respect to $u$ is $dy/du = 2u$, the derivative of $u$ with respect to $x$ is $du/dx = 4$, and to find $dy/dx$, we use the chain rule: $dy/dx = (dy/du) \cdot (du/dx) = 2u \cdot 4 = 8u$. Substituting $u = 4x + 7$ into $8u$, we get $dy/dx = 8(4x + 7) = 32x + 56$.

Find dy/du,du/dx, and dy/dxd y / d u , d u / d x \text {, and } d y / d xdy/du,du/dx, and dy/dx

Find $d y / d u , d u / d x \text {, and } d y / d x$