# What is the derivative of sin x cos x?

Derivatives are very important concepts in mathematics. They have various applications in almost every discipline of engineering and science. They are also used to find the maximum or minimum values of a given function and are also used to predict the monotonicity of a function. Let's solve a question related to derivatives.

## Answer: The derivative of sin x cos x is cos^{2}x - sin^{2}x, that is, cos 2x.

Let's understand how we arrived at the solution.

**Explanation:**

The derivative of sin x cos x can be found by using the product rule of derivatives.

Derivative of u.v = (derivative of u).v + u.(derivative of v)

Let u = sin x and v = cos x

Therefore, using the formula above, we get:

Derivative of sin x.cos x = (derivative of sin x).cos x + sin x.(derivative of cos x)

Therefore, derivative of sin x cos x = cos^{2}x - sin^{2}x = cos 2x

Also, check out the online derivative calculator to verify your answer.

### Hence, the derivative of sin x.cos x is cos^{2}x - sin^{2}x, that is, cos 2x.

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