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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