`y = 1/(5x + 1)` Find the second derivative of the function.

Textbook Question

Chapter 2, Review - Problem 72 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

`y = 1/(5x+1) = (5x+1)^-1`

` `

`differentiating`

`y' = -1{(5x+1)^-2}*5`

`or, y' = -5(5x+1)^-2`

``Differentiating againg w.r.t 'x' we get

`y'' = 10*5*(5x+1)^-3`

`or, y'' = 50/(5x+1)^3`

``

loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

Using a Quotient rule:

Given,

`y=a/b `

Then,

`y'=((a')(b)-(a)(b'))/b^2 `

Therefore,

`y' = ((0)(5x+1)-(1)(5))/(5x+1)^2 `

Simplify,

`y'=-5/(5x+1)^2 `

Take the derivative again

`y''=((0)(5x+1)^2-(-5)(2)(5x+1)(5))/(5x+1)^4 `

Simplify,

`y''=50/(5x+1)^3 `

Note that you should get the same answer if you used a product rule by bringing 5x+1 up with a negative exponent. If you don't, then check your answer because you must have made a mistake along the way.

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