The Chain Rule: Finding the Derivative of f(tan(x)) using the Chain Rule and Sec^2(x)

f'(tanx)

To find the derivative of f(tan(x)), we can use the chain rule

To find the derivative of f(tan(x)), we can use the chain rule. The chain rule states that if we have a composite function, f(g(x)), the derivative of this function is given by f'(g(x)) * g'(x).

Let’s apply this rule to f(tan(x)):
Let u = tan(x). Then, f(tan(x)) can be written as f(u).
Differentiating f(u) with respect to u will give us f'(u).
Differentiating u = tan(x) with respect to x will give us u’ = sec^2(x).

Now, applying the chain rule:
f'(tan(x)) = f'(u) * u’
= f'(tan(x)) * sec^2(x)

So, the derivative of f(tan(x)) is f'(tan(x)) multiplied by sec^2(x).

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