Understanding the Derivative of Cos x | Exploring the Relationship with -Sin x

The derivative of cos x is…

The derivative of cos x is -sin x

The derivative of cos x is -sin x.

To understand why, let’s go over the definition of a derivative. The derivative of a function represents how the function’s output (y-value) changes with respect to its input (x-value). In other words, the derivative measures the rate at which a function is changing at any given point.

In the case of the cosine function, cos x, we can find its derivative using the trigonometric identity:

(d/dx) cos x = – sin x.

This identity states that the derivative of the cosine function is equal to the negative of the sine function. By differentiating the cosine function with respect to x, we obtain the sine function. Hence, the derivative of cos x is -sin x.

Symbolically, we can express it as:

d/dx (cos x) = – sin x.

Therefore, wherever you have the cosine function, the derivative will always give you the negative of the sine function.

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