The Derivative of the Cosine Function | A Step-by-Step Guide to Calculating and Understanding d/dx(cos(x))

cos(x) derivative

The derivative of the cosine function, cos(x), is calculated as follows:

Let’s consider the derivative with respect to x, denoted as d/dx(cos(x))

The derivative of the cosine function, cos(x), is calculated as follows:

Let’s consider the derivative with respect to x, denoted as d/dx(cos(x)). Using the chain rule, we can find the derivative of cos(x) by multiplying the derivative of the inner function (x) with the derivative of the outer function (cos(u)).

The derivative of the inner function, dx/dx, is simply 1.

The derivative of the outer function, d/d(u)(cos(u)), is -sin(u). Since our inner function is x, we can substitute u = x in this case.

Putting it all together, we have:

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

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

In short:

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

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