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

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Answer 1 · 2017-03-19T18:07:06

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

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#