Understanding the Chain Rule: Derivative of cos(x) with Respect to x is -sin(x)

ddx 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)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

In this case, f(u) = cos(u) and g(x) = x. So, we can rewrite cos(x) as f(g(x)) = f(u) = cos(u), with u = x.

Now, let’s find the derivatives of f(u) and g(x):

The derivative of f(u) = cos(u) with respect to u is given by f'(u) = -sin(u).

The derivative of g(x) = x with respect to x is simply g'(x) = 1.

Now, using the chain rule:

ddx (cos(x)) = f'(g(x)) * g'(x).

Substituting the derivatives we found:

ddx (cos(x)) = -sin(g(x)) * 1.

Since g(x) = x, we can rewrite the equation as:

ddx (cos(x)) = -sin(x).

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

More Answers: