How do you differentiate $f(x)=1/x+1/x^3$ using the sum rule?

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Answer 1 · 2015-12-22T12:18:00

$f'(x)=-(x^2+3)/x^4$

Find the derivative of each individual part using the power rule:

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

Thus,

$f'(x)=d/dx[x^-1]+d/dx[x^-3]$

$f'(x)=-x^-2-3x^-4$

$f'(x)=-1/x^2-3/x^4$

This can also be written as:

$f'(x)=-(x^2+3)/x^4$

How do you differentiate f(x)=1/x+1/x^3f(x)=1/x+1/x^3 using the sum rule?