Calculus I - Derivatives

Differentiate the following function $f\left(x\right)=\left(x-5\right)\left(x^2+1\right)$  

•  $f'\left(x\right)=3x^2+10x+1$  

•  $f'\left(x\right)=4x^2+3x+1$  

•  $f'\left(x\right)=3x^2-10x+1$  

•  $f'\left(x\right)=3x^2-10x$  

Differentiate the following function $h\left(t\right)=\frac{t^4-2t^2+7t}{t^3}$  

•  $h'\left(x\right)=1+2t^2+14t^3$  

•  $h'\left(x\right)=1+2t^{-2}-14t^{-3}$  

•  $h'\left(x\right)=2t^{-2}-14t^{-3}$  

•  $h'\left(x\right)=1+t^{-2}-t^{-3}$  

Differentiate the function

  $g\left(x\right)=x^3-\frac{1}{x^6}+\frac{1}{\sqrt{x^5}}$  

•  $g'\left(x\right)=3x^2+6x^{-7}+\frac{3}{2}x^{-\frac{5}{2}}$  

•  $g'\left(x\right)=3x^2+6x^7+\frac{5}{2}x^{-\frac{7}{2}}$  

•  $g'\left(x\right)=3x^2+6x^{-7}-\frac{5}{2}x^{-\frac{7}{2}}$  

•  $g'\left(x\right)=3x^2-6x^7+\frac{5}{2}x^{-\frac{1}{2}}$  

Differentiate the following function $f\left(x\right)=\left(x-\frac{2}{x}\right)\left(7-2x^3\right)$  

•  $f'\left(x\right)=-8x^3+8x+\frac{14}{x^2}+7$  

•  $f'\left(x\right)=8x^3-8x+\frac{14}{x^{ }}+7$  

•  $f'\left(x\right)=8x+\frac{14}{x^2}+7$  

•  $f'\left(x\right)=-8x^4+8x^2+\frac{14}{x^2}+7$  

Differentiate the following function $V\left(x\right)=\frac{1-10t+t^2}{5t+2t^3}$  

•  $V'\left(x\right)=\frac{2x^4+40x^3+x^2-5}{\left(5x+2x^3\right)^2}$  

•  $V'\left(x\right)=\frac{-2x^4-40x^3-x^2-5}{\left(5x+2x^3\right)^{ }}$  

•  $V'\left(x\right)=\frac{-2x^4-40x^3+x^2+5}{\left(5x+2x^3\right)^2}$  

•  $V'\left(x\right)=\frac{-2x^4+40x^3-x^2-5}{\left(5x+2x^3\right)^2}$