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

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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#