Derivate 2

 $f\left(x\right)=\left(x^3+1\right)^4\ ,\ Df\left(x\right)=?$  

•  $f'\left(x\right)=12x^2$  

•  $f'\left(x\right)=4\left(3x^2+1\right)^3$  

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

•  $f'\left(x\right)=4\left(x^3+1\right)^3\cdot3x^2$  

 $f\left(x\right)=\sqrt{\left(x^2+1\right)},\ Df\left(x\right)=?$  

•  $f'\left(x\right)=\frac{1}{2\sqrt{x^2+1}}$  

•  $f'\left(x\right)=\frac{x}{2\sqrt{x^2+1}}$  

•  $f'\left(x\right)=\frac{x}{\sqrt{x^2+1}}$  

•  $f'\left(x\right)=\frac{x}{x^2+1}$  

 $f\left(x\right)=\left(x^2+3x+2\right)^4,\ Df\left(x\right)=?$  

•  $f'\left(x\right)=8x^7+12x$  

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

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

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

 $f\left(x\right)=\frac{1}{\left(x^4+2x+1\right)^3},\ Df\left(x\right)=?$  

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

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

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

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

 $f\left(x\right)=e^x-x^3+3$  

•  $f'\left(x\right)=e^x+3$  

•  $f'\left(x\right)=e^x-3x^2$  

•  $f'\left(x\right)=e^x-x^2+3$  

•  $f'\left(x\right)=x-3$  

 $f\left(x\right)=x+\ln x$  

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

•  $f'\left(x\right)=x+1$  

•  $f'\left(x\right)=\frac{x+1}{x}$  

•  $f'\left(x\right)=x-\frac{1}{x}$  

 $f\left(x\right)=\frac{x}{x^2+1},\ Df\left(x\right)=?$  

•  $f'\left(x\right)=\frac{\left(3x^2+1\right)}{\left(x^2+1\right)}$  

•  $f'\left(x\right)=\frac{\left(2x^2-1\right)}{\left(x^2+1\right)^2}$  

•  $f'\left(x\right)=\frac{\left(1-x^2\right)}{\left(x^2+1\right)^2}$  

•  $f'\left(x\right)=\frac{\left(x^2-1\right)}{\left(x^2+1\right)^2}$  

 $f\left(x\right)=\frac{x}{e^x},\ Df\left(x\right)=?$  

•  $f'\left(x\right)=\frac{1}{e^{2x}}$  

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

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

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

 $f\left(x\right)=xe^x+2x^3+1,\ Df\left(x\right)=?$  

•  $f'\left(x\right)=e^x+6x^2$  

•  $f'\left(x\right)=e^x+xe^x+6x^2$  

•  $f'\left(x\right)=e^x+x+6x^2$  

•  $f'\left(x\right)=xe^x+6x^2$  

 $f\left(x\right)=x^2\cdot\ln x,\ Df\left(x\right)=?\$  

•  $f'\left(x\right)=2x\cdot\ln x$  

•  $f'\left(x\right)=2x\cdot\ln x+x^2$  

•  $f'\left(x\right)=2x\cdot\ln x+x$  

•  $f'\left(x\right)=2x\cdot\ln x+\ln x$