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Derivatives / Product Rule / Logs and Exponentials (14 questions)

QuestionAnswer
Differentiate: $3x^2 \ln(x)$ $6x \ln(x) + 3x$
Differentiate $x e^{-x^2}$ $(1-2x^2) e^{-x^2}$
Differentiate $x \ln(x) -x$ $\ln(x)$
Differentiate $x^3 \ln(x)$ $3x^2 \ln(x) + x^2$
Differentiate $2 x \ln(x)$ $2 \ln(x) + 2$
Differentiate $xe^{4x}$ $e^{4x} + 4xe^{4x}$
Differentiate $10xe^{x}$ $10e^x(1 + x)$
Differentiate $x^2 \ln(5x)$ $2x \ln(5x) + x$
Differentiate $\ln(x) e^x$ $e^x (\ln(x) + \frac{1}{x})$
Differentiate $2x^3 e^x$ $2x^2 e^x(x+3)$
Differentiate $2x^3 e^x$ $2x^2 e^x(x+3)$
Differentiate $x e^{2x}$ $e^{2x}(1+2x)$
Differentiate $e^{2x}(x^2+x)$ $e^{2x}(2x^2+4x+1)$
Differentiate $3x e^{-x}$ $3e^{-x}(1-x)$