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Derivatives / Logarithms (26 questions)

QuestionAnswer
Differentiate: $3x^2 \ln(x)$ $6x \ln(x) + 3x$
Differentiate $\cos(\ln(x))$ $\frac{-\sin(\ln(x))}{x}$
Differentiate $\ln(x^3)$ $\frac{3}{x}$
Differentiate $\ln(x + x^2)$ $\frac{1 + 2x}{x+x^2}$
Differentiate $x \ln(x) -x$ $\ln(x)$
Differentiate $\ln(\cos(x))$ $-\tan(x)$
Differentiate $2 \ln(x^2 + x) + x^3$ $\frac{4x+2}{x^2 + x} + 3 x^2$
Differentiate $x^3 \ln(x)$ $3x^2 \ln(x) + x^2$
Differentiate $\ln(\sin(x))$ $\cot(x)$
Differentiate $\sqrt{\ln(x)}$ $\frac{1}{2 x \sqrt{\ln(x)}}$
Differentiate $\ln(\sqrt{x})$ $\frac{1}{2 \ln(x)}$
Differentiate $\ln(e^x - x^2)$ $\frac{e^x - 2x}{e^x - x^2}$
Differentiate $\ln(e^x x^2)$ $1 + \frac{2}{x}$
Differentiate $2 x \ln(x)$ $2 \ln(x) + 2$
Differentiate $\frac{x}{\ln(x)}$ $\frac{\ln(x)-1}{(\ln(x))^2}$
Differentiate $\ln(x^2 + 3)$ $\frac{2x}{x^2+3}$
Differentiate $\ln(e^{7x})$ $7$
Differentiate $\sqrt{\ln(x)}$ $\frac{1}{2 x \sqrt{\ln(x)}}$
Differentiate $\frac{x}{1+\ln(x)}$ $\frac{\ln(x)}{(1+\ln(x))^2}$
Differentiate $x^2 \ln(5x)$ $2x \ln(5x) + x$
Differentiate $\ln(3x^2)$ $\frac{2}{x}$
Differentiate $\ln(\ln(x))$ $\frac{1}{x \ln(x)}$
Differentiate $\ln(\tan(x))$ $\frac{1}{\sin(x) \cos(x)}$
Differentiate $\ln(4 x^3 + x)$ $\frac{12x^2+1}{4x^3+x}$
Differentiate $\ln(x) e^x$ $e^x (\ln(x) + \frac{1}{x})$
Differentiate $\frac{\ln(x)}{3x^2}$ $\frac{1-2x}{3x^3}$