Question

Using the quotient rule, what is the derivative of the function f(x)=(3x-5)/(5x+2)?​

Answer 1

`(31)/((5x+2)^2)`

Explanation:

See image for quotient rule

f(x)= numerator = 3x-5

g(x)= denominator = 5x+2

so we have

`((5x+2)(3x-5)'-(3x-5)(5x+2)')/((5x+2)^2)\\(3x-5)'=3\\(5x+2)'=5\\((5x+2)(3)-(3x-5)(5))/((5x+2)^2)\\(15x+6-(15x-25))/((5x+2)^2)\\(31)/((5x+2)^2)`