Exponential & Log Derivatives Practice

Find the derivative of  $f\left(x\right)=e^{5x^{5\ }}$  

•  $f'\left(x\right)=25x^4$  

•  $f'\left(x\right)=25x^4e^{5x^{5\ }}$  

•  $f'\left(x\right)=25x^4e^{5x^5-1}$  

•  $f'\left(x\right)=e^{5x^5}$  

Find the derivative of  $f\left(x\right)=\ln\left(4x\right)^5$  

•  $f'\left(x\right)=\frac{5}{x}$  

•  $f'\left(x\right)=\frac{1}{4x^5}$  

•  $f'\left(x\right)=\frac{1}{20x^4}$  

•  $f'\left(x\right)=4x^5$  

Find the derivative of  $f\left(x\right)=\log_4x^2$  

•  $f'\left(x\right)=x^2$  

•  $f'\left(x\right)=\frac{\ln\ 4}{x^2}$  

•  $f'\left(x\right)=\frac{2}{x\ \ln4}$  

•  $f'\left(x\right)=\frac{\ln\ 4}{2x}$  

Find the derivative of  $f\left(x\right)=4^{5x^5}$  

•  $f'\left(x\right)=4^{5x^5}\ln4$  

•  $f'\left(x\right)=25x^4\cdot4^{5x^5}\ln4$  

•  $f'\left(x\right)=25x^4\cdot4^{\left(5x^5-1\right)}\ln4$  

•  $f'\left(x\right)=25x^4$  

Find the derivative of  $f\left(x\right)=\ln\left(\frac{x^3}{x^4+2}\right)^3$  

•  $f'\left(x\right)=3\left(x^3-x^4-2\right)$  

•  $f'\left(x\right)=\frac{4x-3}{4x^3}$  

•  $f'\left(x\right)=\frac{3\left(x^4+2-x^3\right)}{x^3\left(x^4+2\right)}$  

•  $f'\left(x\right)=\frac{-3\left(x^4-6\right)}{x\left(x^4+2\right)}$  

Find the derivative of  $f\left(x\right)=\frac{x^5+1}{e^{5x^{ }}}$  

•  $f'\left(x\right)=\frac{5xe^{5x^2}\left(x^3-2x^5-10\right)}{\left(x^5+5\right)^2}$  

•  $f'\left(x\right)=5\left(x^5+x^4+1\right)$  

•  $f'\left(x\right)=\frac{5\left(x^4-x^5-1\right)}{e^{5x}}$  

•  $f'\left(x\right)=\frac{5x\left(x^3-2x^5-10\right)}{e^{5x^2}}$  

Find the derivative of  $f\left(x\right)=5^{3x^4}\left(x^2-2\right)$  

•  $f'\left(x\right)=2x\cdot5^{3x^4}\left(1+6x^2\ln5\left(x^2-2\right)\right)$  

•  $f'\left(x\right)=2x\left(6x^2\cdot5^{3x^4}\ln5+1\right)$  

•  $f'\left(x\right)=5^{3x^4}\cdot2x$  

•  $f'\left(x\right)=48x^4\cdot5^{3x^4}\ln5$  

Find the derivative of  $f\left(x\right)=\frac{\ln\left(3x\right)}{x^4}$  

•  $f'\left(x\right)=\frac{1-4\ln3x}{x^5}$  

•  $f'\left(x\right)=\frac{1}{x^3}$  

•  $f'\left(x\right)=x^3\left(4\ln x+1\right)$  

•  $f'\left(x\right)=\frac{4\ln3x+1}{x^4}$