How do you find the derivative of $1/(x^2) - 1/x$ ?

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Answer 1 · 2018-01-01T15:29:38

$-2/x^3+1/x^2$

This can be done with the quotient rule, but the easiest thing to do is to first rewrite:

$1/x^2-1/x = x^(-2)-x^(-1)$

$d/dx(1/x^2-1/x) = d/dx(x^(-2)-x^(-1)) = -2x^(-3) -(-1)x^(-2)$
$=-2/x^3+1/x^2$

How do you find the derivative of 1/(x^2) - 1/x1/(x^2) - 1/x?