Exponential and logarithmic derivatives FunctionDerivativeConditions $e^x$$e^x$All real $x$ \(

Question

Exponential and logarithmic derivatives FunctionDerivativeConditions $e^x$$e^x$All real $x$ $a^x$$a^x\ln a$$a>0$ $\ln x$$\dfrac1x$$x>0$ $\log_a x$$\dfrac{1}{x\ln a}$$x>0,\ a>0,\ a\ne1$

Accepted Answer

$\frac{\mathrm d}{\mathrm dx}(e^x)=e^x,\ \frac{\mathrm d}{\mathrm dx}(a^x)=a^x\ln a,\ \frac{\mathrm d}{\mathrm dx}(\ln x)=\frac1x,\ \frac{\mathrm d}{\mathrm dx}(\log_a x)=\frac1{x\ln a}$

Function	Derivative	Conditions
\(e^x\)	\(e^x\)	All real \(x\)
\(a^x\)	\(a^x\ln a\)	\(a>0\)
\(\ln x\)	\(\dfrac1x\)	\(x>0\)
\(\log_a x\)	\(\dfrac{1}{x\ln a}\)	\(x>0,\ a>0,\ a\ne1\)

Exponential and Logarithmic Derivatives

Exponential and Logarithmic Derivatives

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