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

asked Jan 6, 2022 126k views

2 votes

by Keeth

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3 votes

Answer:

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

Explanation:

See image for quotient rule

f(x)= numerator = 3x-5

g(x)= denominator = 5x+2

so we have

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

Murrah answered Jan 11, 2022

4.3k points

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