What is the derivative of #(1-x^2)/(x^3)#?

1 Answer
mason m
May 14, 2016

#(x^2-3)/(x^4)#

Explanation:

Split up the fraction and rewrite it with negative exponents:

#(1-x^2)/x^3=1/x^3-x^2/x^3=x^-3-x^-1#

Now, differentiate #x^-3-x^-1# using the power rule, which states that the derivative of #x^n=nx^(n-1)#. Thus:

#d/dx(x^-3-x^-1)=(-3)x^(-3-1)-(-1)x^(-1-1)#

#=-3x^-4+x^-2#

This is a valid final answer, but we can also write it without negative exponents by multiplying it by #x^4/x^4#:

#(x^4(-3x^-4+x^-2))/x^4=(-3+x^2)/x^4=(x^2-3)/x^4#

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