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How do you find the second derivative of #f(x)=x^(1/2)+x^(-1/2)#?

Answer 1

Paisley Johnson

Find the first derivative, and then differentiate that result again.

#f'(x) = 1/2x^(-1/2) - 1/2x^(-3/2)#

Differentiate:

#f''(x) = -1/4x^(-3/2) + 3/4x^(-5/2)#

#f''(x) = 3/(4x^(5/2)) - 1/(4x^(3/2))#

Hopefully this helps!

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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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