Mastering the Chain Rule: How to Differentiate the Function f(x) = sin(x) with Respect to x

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To differentiate the function f(x) = sin(x) with respect to x, we can use the chain rule of differentiation

To differentiate the function f(x) = sin(x) with respect to x, we can use the chain rule of differentiation. The chain rule states that if we have a composite function g(h(x)), then the derivative of g(h(x)) with respect to x is given by g'(h(x)) multiplied by h'(x).

In this case, the function is f(x) = sin(x), where g(x) = sin(x) and h(x) = x. Since h(x) = x, the derivative of h(x) with respect to x is simply 1. And since g(x) = sin(x), the derivative of g(x) with respect to x is cos(x).

Applying the chain rule, we have:

f'(x) = g'(h(x)) * h'(x)
= cos(x) * 1
= cos(x)

Therefore, the derivative of f(x) = sin(x) with respect to x is f'(x) = cos(x).

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