The Chain Rule: How to Differentiate the Cosine Function (cos(x)) with respect to x

d/dx cosx

To differentiate the cosine function (cos(x)) with respect to x, we can use the chain rule of differentiation

To differentiate the cosine function (cos(x)) with respect to x, we can use the chain rule of differentiation.

The chain rule states that if we have a composite function, y = f(g(x)), where f(u) and g(x) are differentiable functions, then the derivative of y with respect to x is given by dy/dx = f'(u) * g'(x).

In this case, cos(x) is a composite function where the outer function is cosine and the inner function is x itself.

To differentiate, we first find the derivative of the outer function (cosine) and then multiply it by the derivative of the inner function (x).

The derivative of cosine (cos(x)) is found by differentiating the trigonometric function. The derivative of cosine with respect to x is given by -sin(x).

The derivative of x with respect to x is simply 1.

Using the chain rule, we multiply the derivative of the outer function (-sin(x)) by the derivative of the inner function (1).

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

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

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