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Derivatives / Chain Rule / Logs and Exponentials (36 questions)

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