# What is the derivative of #f(x) = (3x+4)/( x^2)#?

##### 1 Answer

Feb 22, 2017

#### Explanation:

dividing each term on the numerator by

#x^2# gives.

#f(x)=(3x)/x^2+4/x^2=3/x+4/x^2=3x^-1+4x^-2# differentiate each term using the

#color(blue)"power rule"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))#

#rArrf'(x)=-3x^-2-8x^-3#

#color(white)(rArrf'(x))=-3/x^2-8/x^3#

#color(white)(rArrf'(x))=-(3x+8)/x^3#