How to Find the Derivative of the Sine Function: Step-by-Step Guide and Explanation

Derivative of sin(x)

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

To find the derivative of the function sin(x), we can use the basic rules of differentiation. The derivative of a function expresses its rate of change at each point.

The derivative of the sine function, denoted as d/dx(sin(x)) or sin'(x), can be found using the chain rule and the derivative of the inside function. Applying the chain rule, we have:

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

Here, the derivative of the inside function is d/dx(x) = 1. Therefore, the derivative of sin(x) is simply:

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

So, the derivative of sin(x) is equal to cos(x). This means that at any point on the graph of sin(x), the slope or rate of change is given by the corresponding value of cos(x).

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