The Derivative of Cos(x): Understanding the Relationship between Sine and Cosine Functions

Derivative of cos(x)

To find the derivative of cos(x), we can use the derivative formula for trigonometric functions

To find the derivative of cos(x), we can use the derivative formula for trigonometric functions. The derivative of cos(x) can be determined by taking the derivative of the sine function (-sin(x)).

The derivative of cos(x) can be written as:

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

We can see that the derivative of cos(x) is equal to the negative of the sine function. This means that at any point on the graph of the cosine function, the slope of the tangent line will be the negative value of the corresponding point on the sine function.

For example, if we take the derivative of cos(x) at x = 0, which is the maximum point on the cosine graph, the derivative will be -sin(0) = 0. This tells us that at x = 0, the slope of the tangent line to the cosine graph is zero. Similarly, if we take the derivative at x = π/2, which is the minimum point on the cosine graph, we get -sin(π/2) = -1. This indicates that at x = π/2, the slope of the tangent line is -1.

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

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