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#