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Derivatives / 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 $\frac{\sqrt{x}}{e^x}$ $\frac{1}{2 \sqrt{x} e^x} - \frac{\sqrt{x}}{e^x}$
Differentiate $\frac{e^x}{x}$ $\frac{xe^x - e^x}{x^2}$
Differentiate $e^{4x}$ $4 e^{4x}$
Differentiate $4e^x$ $4e^x$
Differentiate $e^{x^3+4x}$ $(3x^2 + 4)e^{x^3+4x}$
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 $10xe^{x}$ $10e^x(1 + x)$
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 $\ln(x) e^x$ $e^x (\ln(x) + \frac{1}{x})$
Differentiate $2x^3 e^x$ $2x^2 e^x(x+3)$
Differentiate $2x^3 e^x$ $2x^2 e^x(x+3)$
Differentiate $\frac{e^x}{1+2x}$ $\frac{e^x (2x-1)}{(1+2x)^2}$
Differentiate $x e^{2x}$ $e^{2x}(1+2x)$
Differentiate $\frac{\sin(x)}{e^x}$ $\frac{\cos(x) - \sin(x)}{e^x}$
Differentiate $e^{2x}(x^2+x)$ $e^{2x}(2x^2+4x+1)$
Differentiate $\frac{5x^2}{e^x}$ $\frac{10x-5x^2}{e^x}$
Differentiate $3x e^{-x}$ $3e^{-x}(1-x)$
Differentiate $\frac{e^x}{x^2+2}$ $\frac{e^x(x^2-2x+2)}{(x^2+2)^2}$
Differentiate $\frac{e^2x}{x^2+1}$ $\frac{2e^{2x}(x^2-x+1)}{(x^2+1)^2}$