Question

Find

h ′(2), given that f(2) = −3, g(2) = 4, f ′(2) = −2,and g ′(2) = 5.

I only need help with part d (picture attached)

Answer 1

Answer:
`-(1)/(2)`

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Work Shown:

Apply the quotient rule

`h(x) = (g(x))/(1+f(x))\\\\h(x) = (A)/(B)\\\\h'(x) = (A'*B-A*B')/(B^2)\\\\h'(x) = (g'(x)*(1+f(x))-g(x)*(1+f(x))')/((1+f(x))^2)\\\\h'(x) = (g'(x)*(1+f(x))-g(x)*f'(x))/((1+f(x))^2)\\\\h'(2) = (g'(2)*(1+f(2))-g(2)*f'(2))/((1+f(2))^2)\\\\h'(2) = (5*(1-3)-4*(-2))/((1-3)^2)\\\\h'(2) = (-2)/(4)\\\\h'(2) = -(1)/(2)\\\\`