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

Question

1485 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-05T09:48:01

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

The derivative is linear, that is the derivative of the sum of two functions equals the sum of the derivatives:

$d(f+g)/(dx) = (df)/(dx)+(dg)/(dx)$

Hence:

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

We can evaluate each term using the general rule:

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

so:

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

How do you find the derivative of f(x)=x+1/x^2f(x)=x+1/x^2?