Question

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

Answer 1

Answer:

$\frac{31}{(5x+2)^2}$

Step-by-step explanation:

See image for quotient rule

f(x)= numerator = 3x-5

g(x)= denominator = 5x+2

so we have

$\frac{(5x+2)(3x-5)'-(3x-5)(5x+2)'}{(5x+2)^2}\\(3x-5)'=3\\(5x+2)'=5\\\frac{(5x+2)(3)-(3x-5)(5)}{(5x+2)^2}\\\frac{15x+6-(15x-25)}{(5x+2)^2}\\\frac{31}{(5x+2)^2}$