`f(x) = 1/(x - 6)` Find the second derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 87 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Note:- if y = (ax+b)^n ; where a,b,n are constants ; then dy/dx = an*(ax+b)^(n-1)

Now, 

`f(x) = 1/(x-6) = (x-6)^-1`

`or, f'(x) = -1(x-6)^-2`

`or, f''(x) = 2(x-6)^-3`

`or, f''(x) = 2/(x-6)^3`

` `

loves2learn's profile pic

loves2learn | (Level 3) Salutatorian

Posted on

Using a quotient rule:

Given,

`f(x)=a/b `

Then,

`f'(x)=((a')(b)-(a)(b'))/b^2 `

Therefore,

`f'(x)=((0)(x-6)-(1)(1))/(x-6)^2 `

Simplify,

`f'(x)=-1/(x-6)^2 `

Take the derivative again using a chain rule,

`f''(x)=((0)(x-6)^2-(-1)(2(x-6)))/(x-6)^4 `

Simplify this down, you are left with

`f''(x)=2/(x-6)^3 `

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