Given y = f(u) and u = g(x), find dy/dx = f(g(x))g(x).
-$$\mathrm { y } = \tan \mathrm { u } , \mathrm { u } = - 14 \mathrm { x } + 2$$
A) $- 14 \sec ^ { 2 } ( - 14 x + 2 )$
B) $\sec ^ { 2 } ( - 14 x + 2 )$
C) $- 14 \sec ( - 14 x + 2 ) \tan ( - 14 x + 2 )$
D) $- \sec ^ { 2 } ( - 14 x + 2 )$

Question

Quizplus · Accepted Answer

Using the chain rule, 
$$\frac { d y } { d x } = \frac { d y } { d u } \frac { d u } { d x } = \sec ^ { 2 } u \cdot ( - 14 ) = - 14 \sec ^ { 2 } ( - 14 x + 2 )$$ 
Substituting the given values for y and u in terms of x, we get 
$$\frac { d y } { d x } = \frac { d } { d x } \tan ( - 14 x + 2 ) = \sec ^ { 2 } ( - 14 x + 2 ) \cdot ( - 14 ) = - 14 \sec ^ { 2 } ( - 14 x + 2 )$$ 
Therefore, the correct answer is A.

Given Y = F(u) and U = G(x), Find Dy/dx y=tan⁡u,u=−14x+2\mathrm { y } = \tan \mathrm { u } , \mathrm { u } = - 14 \mathrm { x } + 2y=tanu,u=−14x+2

Given Y = F(u) and U = G(x), Find Dy/dx $\mathrm { y } = \tan \mathrm { u } , \mathrm { u } = - 14 \mathrm { x } + 2$