Derivative of cos(x) with respect to x using the chain rule explained

d/dx(cosx)

To find the derivative of cos(x) with respect to x, we can use the chain rule

To find the derivative of cos(x) with respect to x, we can use the chain rule.

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

In the case of cos(x), we can treat cos(x) as the composite function f(g(x)), where f(u) = cos(u) and g(x) = x.

Differentiating the function f(u) = cos(u) gives us f'(u) = -sin(u).

Now, differentiating the function g(x) = x gives us g'(x) = 1.

Applying the chain rule, we can find the derivative of cos(x) as follows:
d/dx(cos(x)) = f'(g(x)) * g'(x)
= -sin(g(x)) * g'(x)
= -sin(x) * 1
= -sin(x)

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

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