Derivative Help with f(x)= 1/x +1/(x+1)

[helppleasemath]

Homework Statement

[/B]
I have to derivate f(x)

f(x) = 1/x +1/(x+1)

Answer is = -1/x² - 1/(x+1)²
I can't seem to get to that answer :(

thank you

Homework Equations

The Attempt at a Solution

f(x) = (1/x +1/(x+1))'
= (2x+1)/x(x+1)' = ((2x+1)' * (x(x+1)-(2x+1)*(x(x+1)')/x²(x+1)²
=(2(x(x+1)-(2x+1)*(x(1)+(x+1))/x²(x+1)²
=(2x(x+1)-(2x+1)*(2x+1))/x²(x+1)²
=2(x(x+1))-(2x+1)²/x²(x+1)²

 

[brainpushups]

It seems to me that you are doing a bunch of extra work. You don't need to combine the terms over a common denominator to evaluate the derivative because the derivative of a sum is simply the sum of the derivatives.

Differentiate each term separately. If it helps, rewrite the terms with exponents instead of having them as fractions (i.e. write 1/x as x^-1)

 

[member 428835]

Try re-writing $f(x)$ as $f(x)=x^{-1} + (x+1)^{-1}$. From here you can use the chain rule on the second term.

 

[Aceix]

Homework Statement

[/B]f(x) = 1/x +1/(x+1)

Answer is = -1/x² - 1/(x+1)²
I can't seem to get to that answer :(

thank you

Homework Equations

The Attempt at a Solution

f(x) = (1/x +1/(x+1))'
= (2x+1)/x(x+1)' = ((2x+1)' * (x(x+1)-(2x+1)*(x(x+1)')/x²(x+1)²
=(2(x(x+1)-(2x+1)*(x(1)+(x+1))/x²(x+1)²
=(2x(x+1)-(2x+1)*(2x+1))/x²(x+1)²
=2(x(x+1))-(2x+1)²/x²(x+1)²

You actually didn't post a question but from the answer given, the function was differenciated, which is calculus and therefore shouldn't be posted here.

 

[Mark44]

@helppleasemath, minor point, but there is no such word in English as "derivate" at least in the context of calculus. The word you want is "differentiate", the action you perform to get the derivative.

 

[helppleasemath]

@helppleasemath, minor point, but there is no such word in English as "derivate" at least in the context of calculus. The word you want is "differentiate", the action you perform to get the derivative.

oh ok sorry wasnt sure what word to use lol.