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How do you find the derivative of #e^tanx#?

Answer 1

I would use the Chain Rule deriving #e# as it is and then multiplying times the derivative of #tan#, getting: #e^(tan(x))*(1/cos^2(x))#

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Answer 2

Axel Alvarez

To find the derivative of ( e^{\tan(x)} ), you would use the chain rule. The chain rule states that if you have a composite function ( f(g(x)) ), the derivative is ( f'(g(x)) \cdot g'(x) ). In this case, let ( f(u) = e^u ) and ( g(x) = \tan(x) ). Then, ( f'(u) = e^u ) and ( g'(x) = \sec^2(x) ). Applying the chain rule:

[ \frac{d}{dx} (e^{\tan(x)}) = e^{\tan(x)} \cdot \sec^2(x) ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.