Exponential and Logaritmic derivatives

Exponential and Logaritmic derivatives

Calculus Honor

Properties of Exponential and Logarithmic Functions

Derivatives

Log Properties

 $f\left(x\right)=Log\ 2x^2=\log\ 2+\ \ 2\log\ x$  

 $f\left(x\right)=\log_ax=\frac{\log\ x}{\log\ a}$  

 $f\left(x\right)=\log\left(\frac{x}{y}\right)=\log\ x-\ \log\ y$  

f(x)=ln x

y'=1/x

When y=LOGa (x)

Y'=(1/x)ln a

Please Write Power as x^2 for

 $x^2$  

Fill in the Blanks

$$
f\left(x\right)=Ln\ \left(x\ \right)\ \ \ then\ \ \ \ \ \ \ $f\left(x\right)=Ln\ \left(x\ \right)\ \ \ then\ \ \ \ \ \ \ \ \ \$   $Y'=$  

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 $If\ y=\log_2\left(\sqrt{x+2}\right)\ \ \ Then\ \ y'=$  

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 $y=\frac{\ln\ x^2}{2}$  

 Then  Y'=

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 $y=e^{5x}\left(x-1\right)^{\frac{1}{3}}\ \ \ then\ \ \ \ \ \ \ \ \ \ \ \ y'=$  

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 $y=e^{2x}\left(x-1\right)^{\frac{1}{2}}\ \ \ \ \ then\ \ y'=$  

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 $\$   $f\left(x\right)=x\ln\left(x\right)\ \ \ \ \ then\$   $Y'=$  

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  $f\left(x\right)=\ \ln\left(x^5+1\right)\ \ \ Then$   $Y'=$