Continuity and Differentiability

$e^x + e^{-x}$

$e^x - e^{-x}$

$-e^x + e^{-x}$

$0$

$\text{cosec } x \cot x$

$-\text{cosec } x \cot x$

$\text{cosec}^2 x$

$-\cot^2 x$

$\frac{1}{\log x}$

$\frac{1}{x \log x}$

$\frac{x}{\log x}$

$\frac{1}{x}$

$\frac{e^{\sqrt{x^2 + 1}}}{\sqrt{x^2 + 1}}$

$\frac{x e^{\sqrt{x^2 + 1}}}{\sqrt{x^2 + 1}}$

$x e^{\sqrt{x^2 + 1}}$

$\frac{2x e^{\sqrt{x^2 + 1}}}{\sqrt{x^2 + 1}}$

$\frac{\csc^2(\log x)}{x}$

$-\frac{\csc^2(\log x)}{x}$

$-\csc^2(\log x)$

$\frac{\cot(\log x)}{x}$

$6(5 - 4x)^5$

$-24(5 - 4x)^5$

$24(5 - 4x)^5$

$-4(5 - 4x)^5$

$\frac{x}{y}$

$\frac{y}{x}$

$-\frac{y}{x}$

$-\frac{x}{y}$

$\frac{e^x}{\sqrt{1-e^{2x}}}$

$\frac{-e^x}{\sqrt{1-e^{2x}}}$

$\frac{-1}{\sqrt{1-e^{2x}}}$

$\frac{-e^x}{1+e^{2x}}$

$x a^{x-1}$

$a^x \log a$

$\frac{a^x}{\log a}$

$a^x$

$x^{1-x} [\frac{1-x}{x} + \ln x]$

$x^{1-x} [\frac{1-x}{x} - \ln x]$

$(1-x) x^{-x}$

$x^{1-x} [\ln x - \frac{1-x}{x}]$

$(1-x)^x [\ln(1-x) - \frac{x}{1-x}]$

$(1-x)^x [\ln(1-x) + \frac{x}{1-x}]$

$x(1-x)^{x-1}$

$(1-x)^x [\ln(1-x) + 1]$

$7x^6$

$x^7 \ln x$

$7^x \ln 7$

$x^6$

$2/t$

$2t$

$t/2$

$4t$

$\frac{2}{3} \tan \theta$

$\frac{2}{3} \cot \theta$

$-\frac{2}{3} \tan \theta$

$-\frac{2}{3} \cot \theta$

$x/y$

$y/x$

$-x/y$

$-y/x$

$2 \log x + 1$

$2 \log x + 3$

$2 \log x$

$\frac{2}{x}$

$\cot x$

$-\csc^2 x$

$\csc^2 x$

$-\sec^2 x$

$-\frac{3}{x^4}$

$\frac{12}{x^5}$

$-\frac{12}{x^5}$

$\frac{6}{x^5}$