For the following composite function, find an inner function $$ u=g(x) $$ and an outer function $$ y=f(u) $$ such that $$ y=f(g(x)) $$. Then calculate $$ d x= an 4 x^{5} $$ Identify the inner and outer functions. Choose the correct answer. A. $$ u=g(x)=x^{5} $$ and $$ y=f(u)=4 an u $$ B. $$ u=g(x)= an x $$ and $$ y=f(u)=4 u^{5} $$ C. $$ u=g(x)=4 x^{5} $$ and $$ y=f(u)= an u $$ $$ \frac{d y}{d x}=\square=g(x)= an x^{5} $$ and $$ y=f(u)=4 u $$

Question

For the following composite function, find an inner function $$ u=g(x) $$ and an outer function $$ y=f(u) $$ such that $$ y=f(g(x)) $$. Then calculate $$ d x=	an 4 x^{5} $$ Identify the inner and outer functions. Choose the correct answer. A. $$ u=g(x)=x^{5} $$ and $$ y=f(u)=4 	an u $$ B. $$ u=g(x)=	an x $$ and $$ y=f(u)=4 u^{5} $$ C. $$ u=g(x)=4 x^{5} $$ and $$ y=f(u)=	an u $$ $$ \frac{d y}{d x}=\square=g(x)=	an x^{5} $$ and $$ y=f(u)=4 u $$

Lewis Nguyen · Accepted Answer

The inner function is $$ u=g(x)=4x^5 $$ and the outer function is $$ y=f(u)=	an u $$. The derivative $$ \frac{dy}{dx} $$ is $$ 20x^4 \sec^2(4x^5) $$.

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