What is the derivative of $5 + 6/x + 3/x^2$ ?

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Answer 1 · 2016-05-08T09:08:07

$d/(dx) (5+6/x+3/x^2)=-6/x^2-6/x^3$

I find it easiest to think in terms of the exponent form and use the power rule:

$d/(dx) x^n = n x^(n-1)$

as follows:

$d/(dx) (5+6/x+3/x^2)$

$=d/(dx) (5+6x^(-1)+3x^(-2))$

$=0+6((-1)x^(-2))+3((-2)x^(-3))$

$=-6x^(-2)-6x^(-3)$

$=-6/x^2-6/x^3$

What is the derivative of 5 + 6/x + 3/x^25 + 6/x + 3/x^2?