# Differential Functions

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Assume that f/g (x) = x^2 + 2x, where f and g are differentiable functions such that f(2) = 2 and f'(2)= 3. Find g'(2).

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/differential-prime-functions-9018

## SOLUTION This solution is **FREE** courtesy of BrainMass!

f/g(x) = x^2 + 2x.....

or g(x) = f(x)/ (x^2 + 2x) or f(x)*(x^2 + 2x)^-1

g'(x) = f(x)*-1(x^2 + 2x)^-2*(2x+ 2) + f'(x)*(x^2 + 2x)^-1

therefore g'(2)= f(2)*-1(2^2 + 2*2)^-2*(2*2+ 2) + f'(2)*(2^2 + 2*2)^-1

= -2*((8)^-2)*6 + 3*((8)^-1)

= -12/64 + 3/8

= 12/64 or 3/16.

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