Log Function

Trending Questions

Q. If $x^y=e^{x-y},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{at}x=e$ is

1. 1
2. -1
3. $\frac{1}{4}$
4. $\frac{3}{4}$

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Q. If $x^m{y}^n=(x+y{)}^{m+n},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\mathrm{dy}}{\mathrm{dx}}$ is

1. xy
2. $\frac{x}{y}$
3. $\frac{y}{x}$
4. $-\frac{y}{x}$

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Q. If $f\left(x\right)={\log }_x\left(\ln x\right)$, then

1. $f^{\prime }\left(e\right)=e$
2. $f^{\prime }\left(e\right)=\frac{1}{e}$
3. $f^{\prime }\left(e^2\right)=\frac{1}{e^2}$
4. $f^{\prime }\left(e^2\right)=\frac{(1-\ln 2)}{(2e{)}^2}$

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Q. If $y=x^{(\log x{)}^{\log \left(\log x\right)}}$, then $\frac{dy}{dx}$ is

1. $\frac{y}{x}[\ln x^{\ln x-1}+2\ln x\ln (\ln x\left)\right]$
2. $\frac{y}{x\ln x}\left[\right(\ln x{)}^2+2\ln \left(\ln x\right)]$
3. $\frac{y}{x}\left(\log x{)}^{\log \left(\log x\right)}\right(2\log \left(\log x\right)+1)$
4. $\frac{y\log y}{x\log x}\left[2\log \right(\log x)+1]$

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Q. If $x^y=e^{x-y},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{at}x=e$ is

1. 1
2. -1
3. $\frac{1}{4}$
4. $\frac{3}{4}$

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Q. If $x^m{y}^n=(x+y{)}^{m+n},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\mathrm{dy}}{\mathrm{dx}}$ is

1. xy
2. $\frac{x}{y}$
3. $\frac{y}{x}$
4. $-\frac{y}{x}$

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Q. If $y=x^{(\log x{)}^{\log \left(\log x\right)}}$, then $\frac{dy}{dx}$ is

1. $\frac{y}{x}[\ln x^{\ln x-1}+2\ln x\ln (\ln x\left)\right]$
2. $\frac{y}{x\ln x}\left[\right(\ln x{)}^2+2\ln \left(\ln x\right)]$
3. $\frac{y}{x}\left(\log x{)}^{\log \left(\log x\right)}\right(2\log \left(\log x\right)+1)$
4. $\frac{y\log y}{x\log x}\left[2\log \right(\log x)+1]$

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Q. If $f\left(x\right)={\log }_x\left(\ln x\right)$, then

1. $f^{\prime }\left(e\right)=e$
2. $f^{\prime }\left(e\right)=\frac{1}{e}$
3. $f^{\prime }\left(e^2\right)=\frac{1}{e^2}$
4. $f^{\prime }\left(e^2\right)=\frac{(1-\ln 2)}{(2e{)}^2}$

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Q. If $f\left(x\right)={\log }_x\left(\ln x\right)$, then

1. $f^{\prime }\left(e\right)=e$
2. $f^{\prime }\left(e\right)=\frac{1}{e}$
3. $f^{\prime }\left(e^2\right)=\frac{1}{e^2}$
4. $f^{\prime }\left(e^2\right)=\frac{(1-\ln 2)}{(2e{)}^2}$

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Q. If $x^y=e^{x-y},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{at}x=e$ is

1. 1
2. -1
3. $\frac{1}{4}$
4. $\frac{3}{4}$

View Solution