identify-the-inner-ugxu-gx-and-outer-functions-yfuy-fu-for-the-given-composite-f

Question

Identify the inner function $u = g (x)$ , and the outer function $y = f (u)$ for the composition $y = f (g (x))$ . Then, find $\frac{d y}{d x}$ :

$y = (4 x - 1)^{6}$

Accepted Answer

$u = 4 x - 1$ ; $f (u) = u^{6}$ ; $\frac{d y}{d x} = 24 {(4 x - 1)}^{5}$

Answer

$u = 4 x - 1$ ; $f (u) = u^{6}$ ; $\frac{d y}{d x} = 24 {(4 x - 1)}^{5}$

Answer

$u = 4 x - 1$ ; $f (u) = u^{6}$ ; $\frac{d y}{d x} = 24 {(4 x - 1)}^{5}$

Answer

$u = 4 x - 1$ ; $f (u) = u^{6}$ ; $\frac{d y}{d x} = 24 {(4 x - 1)}^{5}$

Identify the inner function u=g(x)u = g(x), and the outer function y=f(u)y = f(u) for the composition y=f(g(x))y = f(g(x)). Then, find dydx\frac{\mathrm{dy}}{\mathrm{dx}}:y=(4x−1)6y = (4x - 1)^6