How to Find the Derivative of Sin(x) Using the Chain Rule and Trigonometric Functions

Derivative of sinx

The derivative of sin(x) can be found using the chain rule and the derivative of the standard trigonometric function

The derivative of sin(x) can be found using the chain rule and the derivative of the standard trigonometric function.

To differentiate sin(x), we first need to recall the derivative of the standard trigonometric function: d/dx(sin(x)) = cos(x).

Now, let’s find the derivative of sin(x):

d/dx(sin(x)) = d/dx(sin(1 * x)) [Using the chain rule]

Applying the chain rule, we can rewrite this as:

d/dx(sin(x)) = cos(1 * x) * d/dx(1 * x) [Applying the chain rule]

d/dx(sin(x)) = cos(x) * 1 [Differentiating 1 * x with respect to x, we get 1]

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

In mathematical notation, we can represent this as:

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

Please note that this derivative represents the rate of change of the sine function with respect to x.

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