Understanding the Chain Rule: Finding the Derivative of cos x with Respect to x

derivative of cos x

The derivative of cos x can be found using the basic rules of differentiation

The derivative of cos x can be found using the basic rules of differentiation. To differentiate cos x, we will use the chain rule. Recall that the chain rule states that if we have a function f(g(x)), the derivative of f(g(x)) with respect to x is equal to f'(g(x)) times g'(x).

In the case of cos x, we can view it as f(g(x)), where f(u) = cos u and g(x) = x. Therefore, applying the chain rule, we have:

d/dx(cos x) = f'(g(x)) * g'(x)

The derivative of f(u) = cos u with respect to u is equal to -sin u. So, f'(g(x)) = -sin(g(x)) = -sin(x). And the derivative of g(x) = x is simply 1.

Substituting these values into the chain rule formula, we have:

d/dx(cos x) = -sin(x) * 1

This simplifies to:

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

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

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