Chain Rule

Chain Rule

 $If\ function\ f\left(x\right)\ =\ \left(ax\ +\ b\right)^n,\$   $then\ the\ derivative\ of\ the\ function\ is$   $f'\left(x\right)=derivative\ of\ \left(ax\ +\ b\right)^n\ times\ derivative\ of\ \left(ax+b\right).$  

 $f'\left(x\right)\ =\ n\ \left(ax\ +\ b\right)^{n-1}\ .\ a$   $\ \ \ \ \ \ \ \ \ \ \ \ \ =\ an\ \left(ax\ +\ b\right)^{n-1}$  

Multiple Choice

 $f\left(x\right)\ =\ \left(2x\ +\ 1\right)^3,\ \ f'\left(x\right)=\ ...$  

•  $3\ \left(2x\ +\ 1\right)^3$  

•  $3\ \left(2x\ +\ 1\right)^2$  

•  $3\ \left(2x\ +\ 1\right)^2\ .\ 2$  

Multiple Choice

 $y\ =\ \left(1\ -\ 3x\right)^7,\ y'\ =\ ...$  

•  $7\ \left(1-3x\right)^6\ -3$  

•  $-21\ \left(1-3x\right)^6$  

•  $4\ \left(1-3x\right)^6$  

Multiple Choice

 $y\ =\ \left(2x\ +\ 3\right)^5,\ \frac{\text{d}y}{\text{d}x}=\ ...$  

•  $5\ \left(2x\ +\ 3\right)^4$  

•  $7\ \left(2x\ +\ 3\right)^4$  

•  $10\ \left(2\ x\ +\ 3\right)^5$  

•  $10\ \left(2x\ +\ 3\right)^4$  

Multiple Choice

 $f\left(x\right)\ =\ \sqrt{x\ +\ 2},\ \ f'\left(x\right)=\ ...$  

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

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

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

Multiple Choice

 $y\ =\ \sqrt{9x\ +1},\ the\ derivative\ of\ y\ is\ ...$  

•  $\left(9x\ +\ 1\right)^{\frac{1}{2}}$  

•  $\frac{9}{2\ }\left(9x\ +\ 1\right)^{-\frac{1}{2}}$  

•  $\frac{1}{2}\left(9x\ +1\right)^{-\frac{1}{2}}$  

Multiple Choice

 $y\ =\ \sqrt{x^2-9},\ \frac{\text{d}y}{\text{d}x}=\ ...$  

•  $\frac{1}{2}\left(x^2\ -\ 9\right)^{-\frac{1}{2}}$  

•  $x\ \left(x^2\ -\ 9\right)^{-\frac{1}{2}}$  

•  $2x\ \left(x^2\ -\ 9\right)^{-\frac{1}{2}}$  

•  $\frac{1}{2x}\left(x^2-9\right)^{-\frac{1}{2}}$