calculate the derivative
(2,5) (2.1,5.3)
h'(2) if h(x)=(f(x))^3
k'(2) if k(x)=f(x))^-1
g'(5) if g(x)=f^-1(x)
To calculate the derivative of a function at a specific point, we use the concept of the derivative as the slope of the tangent line to the function's graph at that point.
Let's proceed with the given functions:
1. h(x) = (f(x))^3
To find h'(2), we first need to find the derivative of f(x) and then substitute x = 2 into the derivative expression.
2. k(x) = (f(x))^-1
To find k'(2), we follow a similar process. We differentiate f(x) and substitute x = 2 into the resulting derivative equation.
3. g(x) = f^(-1)(x)
To find g'(5), we differentiate the inverse function f^(-1)(x) and substitute x = 5.
Since we don't have the explicit form of f(x), we cannot directly compute the derivatives h'(2), k'(2), and g'(5) without assuming the properties of f(x). Please provide the function f(x) or some additional information related to f(x) to proceed with the derivatives of h(x), k(x), and g(x).