Answer
inside: $g(x)= 7 \sin (5 x+4)+3$
outside: $f(g)= (g(x))^2$
derivative: $f^{\prime}(x)=70(7 \sin (5 x+4)+3 )(\cos(5x+4))$
Work Step by Step
Given$$ f(x)=(7 \sin (5 x+4)+3)^{2} $$
Use the chain rule to take the derivative
$$ \frac{d f(g(x))}{d x}=f^{\prime}(g(x)) g^{\prime}(x) $$
Here $g(x)=7 \sin (5 x+4)+3$ and $f(g)= ( g(x) )^{2},$ then
\begin{align*}
f^{\prime}(x) &=\left( (g(x) )^{2}\right)^{\prime} \\
&=2( g(x) )g^{\prime}(x) \\
&=(2)(g(x))(35\cos(5x+4))\\
&=70(7 \sin (5 x+4)+3 )(\cos(5x+4)) \end{align*}
