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Derivatives / Quotient Rule / Logs and Exponentials (10 questions)

QuestionAnswer
Differentiate $\frac{\sqrt{x}}{e^x}$ $\frac{1}{2 \sqrt{x} e^x} - \frac{\sqrt{x}}{e^x}$
Differentiate $\frac{e^x}{x}$ $\frac{xe^x - e^x}{x^2}$
Differentiate $\frac{x}{\ln(x)}$ $\frac{\ln(x)-1}{(\ln(x))^2}$
Differentiate $\frac{x}{1+\ln(x)}$ $\frac{\ln(x)}{(1+\ln(x))^2}$
Differentiate $\frac{e^x}{1+2x}$ $\frac{e^x (2x-1)}{(1+2x)^2}$
Differentiate $\frac{\sin(x)}{e^x}$ $\frac{\cos(x) - \sin(x)}{e^x}$
Differentiate $\frac{5x^2}{e^x}$ $\frac{10x-5x^2}{e^x}$
Differentiate $\frac{e^x}{x^2+2}$ $\frac{e^x(x^2-2x+2)}{(x^2+2)^2}$
Differentiate $\frac{\ln(x)}{3x^2}$ $\frac{1-2x}{3x^3}$
Differentiate $\frac{e^2x}{x^2+1}$ $\frac{2e^{2x}(x^2-x+1)}{(x^2+1)^2}$