Master the Chain Rule: How to Find the Derivative of f(cosx)

f'(cosx)

To find the derivative of a function, we can use the chain rule

To find the derivative of a function, we can use the chain rule. In this case, we want to find the derivative of f(cosx).

Let’s start by defining our function f(u) = u, where u = cosx. So, f(u) = u.

Now, let’s find the derivative of f(u) with respect to u. The derivative of f(u) with respect to u is simply 1, since f(u) = u.

Next, we need to find the derivative of u = cosx with respect to x. To do this, we can use the chain rule.

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

Applying the chain rule to u = cosx, we have:

du/dx = d(cosx)/dx

The derivative of cosine is negative sine, so d(cosx)/dx = -sinx.

Therefore, we have:

du/dx = -sinx

Now, we can use the chain rule to find the derivative of f(cosx) with respect to x.

df/dx = f'(u) * du/dx

Since f(u) = u and f'(u) = 1, we can simplify the above equation to:

df/dx = 1 * (-sinx) = -sinx

Thus, the derivative of f(cosx) with respect to x is -sinx.

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