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Derivatives / Quotient Rule (15 questions)

QuestionAnswer
Differentiate $\frac{3x-2}{2x-3}$ $\frac{-5}{(2x-3)^2}$
Differentiate $\frac{\cos(x)}{1-\sin(x)}$ $\frac{1}{1-\sin(x)}$
Differentiate $\frac{3x^2}{4x^2 + 7x}$ $\frac{21x^2}{(4x^2+7x)^2}$
Differentiate $\frac{x^2}{3x+2}$ $\frac{3x^2+4x}{(3x+2)^2}$
Differentiate $\frac{3-x}{x+3}$ $\frac{-2x}{(x+3)^2}$
Differentiate $\frac{x^3+1}{x-4}$ $\frac{2x^3-12x^2-1}{(x-4)^2}$
Differentiate $\frac{x^2+1}{x^2-1}$ $\frac{-4x}{(x^2-1)^2}$
Differentiate $\frac{2x+5}{3x-2}$ $\frac{-19}{(3x-2)^2}$
Differentiate $\frac{\sqrt{x}-1}{\sqrt{x}+1}$ $\frac{1}{2 \sqrt{x} (\sqrt{x}+1)^2}$
Differentiate $\frac{4x}{3x+2}$ $\frac{2}{(3x+2)^2}$
Differentiate $\frac{x^2+8}{x+4}$ $\frac{x^2+8x-8}{(x+4)^2}$
Differentiate $\frac{3x^2-4}{x+2}$ $\frac{3x^2+12x+4}{(x+2)^2}$
Differentiate $\frac{x^2+8}{6-x}$ $\frac{-x^2+12x+8}{(6-x)^2}$
Differentiate $\frac{\sin(x)+1}{\cos(x)+1}$ $\frac{1+\sin(x) + \cos(x)}{(\cos(x)+1)^2}$
Differentiate $\frac{4x}{3+\sqrt{x}}$ $\frac{12+2\sqrt{x}}{(3+\sqrt{x})^2}$