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

Question

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 - $$1)^6$$

Accepted Answer

u=4x−1u=4x-1; f(u)=u6f\left(u\right)=$$u^6$$; dydx=24(4x−1)5\frac{\mathrm{dy}}{\mathrm{d}x}=24\left(4x-1\$$right)^5$$

Answer

u=4x−1u=4x-1; f(u)=u6f\left(u\right)=$$u^6$$; dydx=24(4x−1)4\frac{\mathrm{dy}}{\mathrm{d}x}=24\left(4x-1\$$right)^4$$

Answer

u=4x−1u=4x-1; f(u)=u5f\left(u\right)=$$u^5$$; dydx=20(4x−1)4\frac{\mathrm{dy}}{\mathrm{d}x}=20\left(4x-1\$$right)^4$$

Answer

u=4x−1u=4x-1; f(u)=u6f\left(u\right)=$$u^6$$; dydx=6(4x−1)5\frac{\mathrm{dy}}{\mathrm{d}x}=6\left(4x-1\$$right)^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

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