Understanding the Derivative of cos(x) | Explained with Detailed Examples

cos(x) is the derivative of?

The derivative of cos(x) is denoted as -sin(x)

The derivative of cos(x) is denoted as -sin(x). Let me explain this in detail:

The derivative of a function measures the rate at which the function is changing at any given point. In the case of trigonometric functions like cos(x), their derivatives also follow certain patterns.

To find the derivative of cos(x), we can use the differentiation rules. The derivative of cos(x) can be obtained using the chain rule, as follows:

Let’s define y = cos(x).

Now, we need to take the derivative of y with respect to x, denoted as dy/dx.

Using the chain rule, we differentiate the outer function (cos(x)) and multiply it by the derivative of the inner function (x).

The derivative of cos(x) is obtained as follows:

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

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

It is important to note that the negative sign comes from differentiating the cos(x) function, while the sin(x) part represents the derivative of the inner function (x). This is a fundamental property of trigonometric functions.

I hope this explanation helps clarify the concept of finding the derivative of cos(x). If you have any further questions, please feel free to ask!

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