`f(x) = 1/(5x + 1)^2` Find the derivative of the function.

Expert Answers
hkj1385 eNotes educator| Certified Educator

Note :- 1) If y = x^n ; where n = constant, then dy/dx = n*(x^(n-1))

2) If y = n*x ; where n = constant ; then dy/dx = n

Now, 

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

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

`thus, dy/dx = y' = -2*{(5x+1)^-3}*5`

`or, y' = -10/{(5x+1)^3}`

``

loves2learn | Student

Using a Quotient rule:

Given,

Then,

Therefore,

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

Simplifying this all down, you get

`f'(x)=-10/(5x+1)^3 `

Note that you should get the same answer if you used a product rule by bringing `(5x+1)^2` up with a negative exponent into `(5x+1)^-2 ` . If you don't, then check your answer because you must have made a mistake along the way.