Mathematics

Problem

Suppose a classmate claims that an antiderivative of the function

f(x)=\frac{3x^{2}}{(x^{3}+1)^{5/2}}

F(x)=-(x^{3}+1)^{-3/2}+C,

where

C

is an arbitrary constant. a. Differentiate

F(x)

explicitly and simplify the result. b. Compare your derivative to

f(x)

. State whether the classmate’s claim is correct and justify your conclusion in complete sentences.