Find the derivative.
-$\frac{x-3}{(2 x+5)(3 x+5)}$
A) $\frac{6 x^{2}-14 x+100}{(2 x+5)^{2}(3 x+5)^{2}}$
B) $\frac{-6 x^{2}+36 x+100}{(2 x+5)(3 x+5)}$
C) $\frac{6 x^{2}-14 x+100}{(2 x+5)(3 x+5)}$
D) $\frac{-6 x^{2}+36 x+100}{(2 x+5)^{2}(3 x+5)^{2}}$

Question

Quizplus · Accepted Answer

The derivative is found using the quotient rule and product rule. The correct derivative simplifies to the expression in choice D.

Find the Derivative x−3(2x+5)(3x+5)\frac{x-3}{(2 x+5)(3 x+5)}(2x+5)(3x+5)x−3​ A) 6x2−14x+100(2x+5)2(3x+5)2\frac{6 x^{2}-14 x+100}{(2 x+5)^{2}(3 x+5)^{2}}(2x+5)2(3x+5)26x2−14x+100​

Find the Derivative $\frac{x-3}{(2 x+5)(3 x+5)}$ A) $\frac{6 x^{2}-14 x+100}{(2 x+5)^{2}(3 x+5)^{2}}$