How do you find the derivative of #y=tanh(6+e^(6x))#?

Answer 1

Ezekiel Alexander

Simple application of the chain rule.

#d/(du)(tanh(u)) = sech^2(u)#

#(dy)/(dx) = (dy)/(du)*(du)/(dx)#

So #sech^2(6+e^(6x))*d/(dx)(6+e^(6x))#

#(dy)/(dx) = 6*e^(6x)*sech^2(6+e^(6x))#

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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.

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