The Chain Rule: Calculating the Derivative of sin(x) Using Basic Derivative Rules

d/dx [ sin(x) ]

To find the derivative of sin(x), we can use the basic derivative rules

To find the derivative of sin(x), we can use the basic derivative rules. The derivative of sin(x) can be calculated using the chain rule.

The chain rule states that if we have a composite function, f(g(x)), then the derivative of f(g(x)) with respect to x is equal to f'(g(x)) * g'(x).

In this case, f(x) = sin(x) and g(x) = x.

We know that the derivative of sin(x) is cos(x) and the derivative of x is 1.

Using the chain rule, we can find the derivative of f(g(x)):

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

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

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