How to Find the Derivative of f(sin(x)) Using the Chain Rule: Step-by-Step Guide

f'(sinx)

To find the derivative of f(sin(x)), we can use the chain rule

To find the derivative of f(sin(x)), we can use the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, our outer function is f(x) and our inner function is sin(x). So, let’s find the derivatives of both functions:

1. Derivative of f(x):
The derivative of f(x) is represented as f'(x). Since we don’t have any specific information about the function f(x), we can’t find its derivative without additional information, such as the function itself or its equation.

2. Derivative of sin(x):
The derivative of sin(x) is found by differentiating the trigonometric function. The derivative of sin(x) with respect to x is cos(x), which means that d/dx(sin(x)) = cos(x).

Now, let’s combine these two derivatives using the chain rule. According to the chain rule, the derivative of f(sin(x)) is:

d/dx(f(sin(x))) = f'(sin(x)) * d/dx(sin(x))

Substituting the known derivatives:

d/dx(f(sin(x))) = f'(sin(x)) * cos(x)

Therefore, the derivative of f(sin(x)) is f'(sin(x)) * cos(x).

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