How do you find the derivative of rational functions: #(3/x)#, #(7/x^2)#, #(x^3/sqrt(x))#?

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Answer 1 · 2015-02-08T19:31:31

You can use the Quotient Rule or rewrite them as powers, as in:

#3/x=3x^-1#
Derived: #3*(-1)*x^(-1-1)=-3x^-2=-3/x^2#

and:

#7/x^2=7x^-2#
Derived: #7*(-2)*x^(-2-1)=-14x^-3=-14/x^3#

and:

#x^3/sqrt(x)=x^3*x^(-1/2)=x^(5/2)#
Derived: #5/2x^(5/2-1)=5/2x^(3/2)=5/2xsqrt(x)#

hope it helps