Understanding the Chain Rule for Finding the Derivative of Sin(x)

Derivative of sin(x)

The derivative of sin(x) is found by applying the chain rule

The derivative of sin(x) is found by applying the chain rule.

The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative of this composition is given by the product of the derivative of the outer function and the derivative of the inner function.

In this case, the outer function is sin(x) and the inner function is x.

The derivative of the outer function sin(x) is found by applying the derivative of the sine function, which is cos(x).

The derivative of the inner function, x, is simply 1.

Applying the chain rule, we have:

d/dx(sin(x)) = cos(x) * 1 = cos(x)

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

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