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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