Determine a function #h# such that #d/(dx)[sqrt(h(x))] = (3x^2)/(2sqrt(x^3+4))?#

1 Answer
Mar 19, 2017

#h(x) = x^3+4#

Explanation:

Given:

#d/(dx)[sqrt(h(x))] = (3x^2)/(2sqrt(x^3+4))#

Applying the chain rule to the left side:

#1/(2sqrt(h(x)))h'(x) = (3x^2)/(2sqrt(x^3+4))#

Matching the argument under the radical:

#h(x) = x^3+4#

Confirmed by #h'(x) = 3x^2#