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Single Variable Calculus

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Moderate

Derivative of a Rational Function: Chain Rule and Quotient Rule

SVCALC-WSQ7PJ

Find the derivative of:

$$f(x)=\dfrac{(5x-2)^3}{(3x+2)^4}$$

Factor and simplify the final answer.

A

$-\dfrac{15(5x-2)^2}{(3x+2)^5}$

B

$\dfrac{15(5x-2)^2}{12(3x+2)^3}$

C

$\dfrac{3(5x-2)^2}{4(3x+2)^3}$

D

$-\dfrac{3(5x-2)^2(5x-18)}{(3x+2)^5}$