Finding the Derivative of Sin(x) and its Definition – A Math Tutorial

Derivative of sin(x)

The derivative of the sine function, sin(x), can be found using the definition of the derivative

The derivative of the sine function, sin(x), can be found using the definition of the derivative.

The derivative of a function is a measure of how the function changes as its input (x) changes. It is represented using the symbol “d/dx” or “f'(x)”, where “f” is the function and “x” is the variable.

To find the derivative of sin(x), we start by recalling the derivative of the basic trigonometric function cosine, cos(x). The derivative of cos(x) is -sin(x), as established in trigonometry.

Using this derivative, we can find the derivative of sin(x) by differentiating the derivative of cos(x) with respect to x.

Therefore, the derivative of sin(x) is:

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

So, the derivative of sin(x) is equal to cos(x).

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