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How do you differentiate #f(x)=e^(sinsqrtx)# using the chain rule.?

Answer 1

Ezra Adams

#d/dx e^(sin sqrt(x)) = frac (cos sqrt x) (2 sqrt x) e^(sin sqrt(x)) #

#(df)/(dx) = (d(e^(sin sqrt(x))))/(d(sin sqrt(x))) * (d(sin sqrt(x)))/(d sqrt x) * (d sqrt x)/(dx)#

#(df)/(dx) = e^(sin sqrt(x)) * cos sqrt x * 1/2 1/sqrt x#

#(df)/(dx) = frac (cos sqrt x) (2 sqrt x) e^(sin sqrt(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.

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