f(0)=7, g(0)=5, f'(0)-=-12, and g'(0)=5. Find h'(0) for the function h(x)=f(x)/g(x)

To find h'(0) for the function h(x) = f(x)/g(x), we need to use the quotient rule, which states that if we have two functions f(x) and g(x), the derivative of their quotient h(x) = f(x)/g(x) is given by:

h'(x) = (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2.

In this case, we are given that f(0) = 7, g(0) = 5, f'(0) = -12, and g'(0) = 5. We want to find h'(0).

Using the quotient rule formula, we substitute the given values into the formula:

h'(x) = (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2
h'(0) = (f'(0) * g(0) - f(0) * g'(0)) / (g(0))^2

Substituting the given values:

h'(0) = (-12 * 5 - 7 * 5) / (5)^2

Simplifying:

h'(0) = (-60 - 35) / 25

h'(0) = -95 / 25

h'(0) = -3.8

Therefore, h'(0) for the function h(x) = f(x)/g(x) is -3.8.