Suppose that f(2) = −3, g(2) = 5, f '(2) = −2, and g'(2) = 4. Find h'(2)? h(x) = g(x) / 1 + f(x)

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Answer 1 · 2017-10-11T20:41:38

#h'(2) = 1/2#

I'm assuming that

#h(x) = (g(x))/(1 + f(x))#

Then by the quotient rule, the derivative is given by

#h'(x) = (g'(x)(1 + f(x)) - (f'(x)g(x)))/(1 + f(x))^2#

So

#h'(2) = (g'(2)(1 + f(2)) - (f'(2)g(2)))/(1 + f(2))^2#

We can now evaluate directly.

#h'(2) = (4(1 - 3) - (-2)(5))/(1 - 3)^2#

#h'(2) = (-8 + 10)/4#

#h'(2) = 1/2#

Hopefully this helps!