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How do you find the second derivative of # ln(x^2+10)# ?

Answer 1

Paisley Johnson

#(d^2y)/(dx^2) = (2(10 - x^2))/(x^2 + 10)^2#

We find the first derivative , and then differentiate again.

#y = ln(x^2 + 10)#

#e^y = x^2 + 10#

#e^y(dy/dx) = 2x#

#dy/dx= ( 2x)/(e^(y)#

#dy/dx= (2x)/(e^ln(x^2 + 10)#

#dy/dx = (2x)/(x^2 + 10)#

#(d^2y)/(dx^2) = (2(x^2 + 10) - 2x(2x))/(x^2 + 10)^2#

#(d^2y)/(dx^2) = (2x^2 + 20 - 4x^2)/(x^2 + 10)^2#

#(d^2y)/(dx^2) = (2(10 - x^2))/(x^2 + 10)^2#

Hopefully this helps!

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Answer 2

William Abdalla

To find the second derivative of ln(x^2+10), you first find the first derivative, then differentiate that result to find the second derivative. The first derivative is (2x)/(x^2+10), and the second derivative is [(2(x^2+10) - 2x(2x)] / (x^2+10)^2. Simplifying, you get the second derivative as (-4x^2 + 20) / (x^2+10)^2.

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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.