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

Answer 1

Charles Anctil

#f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)#

According to the chain rule,

#f'(x)=e^(secsqrtx)d/dx[secsqrtx]#

First, find the internal derivative (again using the chain rule).

#d/dx[secsqrtx]=secsqrtxtansqrtxd/dx[sqrtx]#

#=1/2x^(-1/2)secsqrtxtansqrtx#

#=(secsqrtxtansqrtx)/(2sqrtx)#

Plug this back in to find #f'(x)#.

#f'(x)=(e^(secsqrtx))(secsqrtxtansqrtx)/(2sqrtx)#

#f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)#

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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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