Answer
$(a) (f\circ g)(x)=(2x-3)^5, (f\circ g)'(x)=10(2x-3)^4$
$(b) (g \circ f)(x)=2x^5-3, (g\circ f)'(x)=10x^4$
Work Step by Step
$f(x)=x^5, g(x)=2x-3$
$(a)$ $(f \circ g)(x)=f(g(x))=f(2x-3)=(2x-3)^5$
$(f\circ g)'(x)=((2x-3)^5)'=5(2x-3)^4\cdot(2x-3)'=5(2x-3)^4\cdot2=10(2x-3)^4$
$(b) (g\circ f)(x)=g(f(x))=g(x^5)=2x^5-3$
$(g\circ f)'(x)=(2x^5-3)'=2\cdot5x^4-0=10x^4$
