Understanding the Derivative of cos(x) with Respect to x using the Chain Rule

d/dx(cosx)

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

To compute the derivative of cos(x) with respect to x, we can use the chain rule. The chain rule states that if we have a function, g(f(x)), then the derivative of g(f(x)) with respect to x is given by g'(f(x)) * f'(x).

For cos(x), the outer function is g(u) = cos(u), and the inner function is f(x) = x. The derivative of the outer function, g'(u), is equal to -sin(u), and the derivative of the inner function, f'(x), is equal to 1.

Using the chain rule, the derivative of cos(x) with respect to x is:

d/dx(cosx) = g'(f(x)) * f'(x)
= -sin(x) * 1
= -sin(x)

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

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