Find the derivative of a logarithmic function Calculus

Find the derivative of the following functions.

f:x\longmapsto \log_{3}\left(x\right)

f'\left(x\right)=\dfrac{1}{3x\cdot\log_3\left(x\right)}

f'\left(x\right)=\dfrac{1}{3x}

f'\left(x\right)=\dfrac{ln\left(3\right)}{x}

f'\left(x\right)=\dfrac{1}{x\cdot\ln\left(3\right)}

f:x\longmapsto \ln\left(x\right)

f'\left(x\right)=\dfrac{1}{x\cdot \ln\left(x\right)}

f'\left(x\right)=\dfrac{1}{x}

f'\left(x\right)=\dfrac{1}{ex}

f'\left(x\right)=e^{x}\ln\left(x\right)

f:x\longmapsto 5\log\left(x\right)

f'\left(x\right)=\dfrac{5}{x\ln\left(10\right)}

f'\left(x\right)=\dfrac{5}{x}

f'\left(x\right)=\dfrac{1}{x\ln\left(10\right)}

f'\left(x\right)=\dfrac{5\ln\left(10\right)}{x}

f:x\longmapsto 4\log_{2}\left(3x\right)

f'\left(x\right)=\dfrac{12}{x\ln\left(2\right)}

f'\left(x\right)=\dfrac{12}{x}

f'\left(x\right)=\dfrac{4}{x\ln\left(2\right)}

f'\left(x\right)=\dfrac{4}{x\log_{2}\left(3\right)}

f:x\longmapsto \dfrac{1}{3}\log_{\frac{1}{9}}\left(x\right)

f'\left(x\right)=\dfrac{3}{x\ln\left(9\right)}

f'\left(x\right)=\dfrac{3}{x\ln\left(3\right)}

f'\left(x\right)=\dfrac{\ln\left(3\right)}{x\ln\left(9\right)}

f'\left(x\right)=-\dfrac{1}{3x\ln\left(9\right)}

f:x\longmapsto e^{2}\ln\left(x\right)

f'\left(x\right)=\dfrac{e^{2}}{x}

f'\left(x\right)=\dfrac{2e}{x}

f'\left(x\right)=2e\ln\left(x\right)+\dfrac{e^{2}}{x}

f'\left(x\right)=2e\ln\left(x\right)