How to find the derivative for f(x)= 5x+1/x, x=-1

Question

anonymous · Answer

you have a choice. 
a) you can use the annoying quotient rule 
$$(\frac{f}{g})'=\frac{gf'-fg'}{g^2}$$ or you can write 
$$f(x)=5-\frac{1}{x}$$ and take the derivative of that, which is much simpler

anonymous · Answer

oops last line should have been 
$$f(x)=5+\frac{1}{x}$$

anonymous · Answer

you go (5x+1)*x^-1 and then take derivative

anonymous · Answer

derivative of a constant is 0
derivative of $\frac{1}{x}$ is $-\frac{1}{x^2}$ replace x by $-1$ to get your answer

anonymous · Answer

mathdood method would work, but i would not recommend it
easier just to divide each term by x and go from there

anonymous · Answer

Okay i know to to solve it with the qoutient rule but not how to solve.it with the derivative rule

anonymous · Answer

no no don't use the quotient rule

anonymous · Answer

the quotient rule is a derivative rule, but you don't want to use it here because there is a much much simpler way

anonymous · Answer

$$f(x)=5+\frac{1}{x}$$
$$f'(x)=-\frac{1}{x}^2$$
$$f'(-1)=-\frac{1}{(-1)^2}=-1$$

anonymous · Answer

But the answer in my textbook is 4.....

anonymous · Answer

$$ f(x)= 5x+\frac1x$$

$$ f'(x)=5-\frac{1}{x}^2 $$
$$ f'(-1)=5-\frac{1}{(-1)^2}=5-1=4$$