Understanding the Chain Rule | Finding the Derivative of Cos(x)

Derivative of:cos(x)

The derivative of the function cos(x) can be found using the chain rule of differentiation

The derivative of the function cos(x) can be found using the chain rule of differentiation.

The chain rule states that if we have a composite function, say f(g(x)), then the derivative of f(g(x)) with respect to x is given by the product of the derivative of f with respect to g(x), and the derivative of g(x) with respect to x.

In this case, f(x) = cos(x) and g(x) = x. So we are interested in finding the derivative of f(g(x)) = cos(x) with respect to x.

To find the derivative, we differentiate f(x) = cos(x) with respect to g(x) which is simply -sin(g(x)). Then, we differentiate g(x) = x with respect to x, which is 1.

Now, we multiply the two derivatives together: -sin(g(x)) * 1 = -sin(x).

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

In summary,
d/dx (cos(x)) = -sin(x).

This derivative tells us how the value of the cosine function changes with respect to the variable x.

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