What is the derivative of f(x)=(4x-1)/x?

2 Answers
Sep 15, 2016

(1) / (x^(2))

Explanation:

We have: f(x) = (4 x - 1) / (x)

This function can be differentiated using the "quotient rule":

=> f'(x) = ((x) (4) - (4 x - 1) (1)) / ((x)^(2))

=> f'(x) = (4 x - 4 x + 1) / (x^(2))

=> f'(x) = (1) / (x^(2))

Sep 15, 2016

f'(x)=1/x^2

Explanation:

Alternatively, we can split up the fraction:

f(x)=(4x-1)/x=(4x)/x-1/x=4-x^-1

Use the power rule, d/dxx^n=nx^(n-1), to differentiate this. Recall that the derivative of the constant is 0.

f'(x)=0-(-x^-2)=1/x^2