Question

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

Answer 1

`f'(x)=-(3x+8)/x^3`

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`