Find the Derivative - d/dx h(x)=f(g(x))

Problem

d()/d(x)*h(x)=ƒ*(g(x))

Solution

1. Identify the structure of the function as a composition of two functions, where ƒ is the outer function and g(x) is the inner function.

2. Apply the Chain Rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

3. Differentiate the outer function ƒ with respect to its argument g(x) to get ƒ′*(g(x))

4. Differentiate the inner function g(x) with respect to x to get g(x)′

5. Multiply the results of the previous steps to obtain the final derivative.

Final Answer

(d(ƒ)*(g(x)))/d(x)=ƒ′*(g(x))*g(x)′

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