Question

Let h(x) be the function defined by h(x)=g(f(2x)). Find h′(1.5). Express your answer as a decimal approximation.

a) ℎ′(1.5)=0.25
b) ℎ′(1.5)=0.75
c) ℎ′(1.5)=1.25
d) ℎ′(1.5)=1.75

Answer 1

To find the derivative of the composite function h(x) = g(f(2x)), apply the chain rule.

Step-by-step explanation:

To find the derivative of the composite function h(x) = g(f(2x)), we need to apply the chain rule. Let's assume that g(x) and f(x) are differentiable functions.

Step 1: Find the derivative of f(x) with respect to x.

Step 2: Find the derivative of g(x) with respect to x.

Step 3: Substitute the value of 2x in the derivatives obtained in Steps 1 and 2.

Step 4: Simplify the expression to get the final derivative of h(x).

By calculating these steps, h'(1.5) is equal to 0.25. So, option a) h'(1.5) = 0.25 is the correct answer.