Differentiation and it's Application: ( Prepared by :NMK)

 $\frac{\text{d}}{\text{d}y}\left(2x^2+5x+7\right)$  

• 5x+2

•  $2x^3+5$  

• 4x+5

• 5+4x

 $find\ \frac{\text{d}y}{\text{d}x}\ for:\ \ y=\left(x+1\right)^2$  

• 2x+2

• 2x+1

• 1+2x

• 2x+4

 $Given\ that\ y=5x+\frac{1}{x^2}calulate\ the\ gradient\ of\ the\ curve\ at\ x=3$  

•  $\frac{145}{23}$  

•  $\frac{27}{133}$  

•  $\frac{55}{27}$  

•  $\frac{133}{27}$  

 $Given\ that\ PV=3600,\ find\ the\ value\ of\ \frac{\text{d}P}{\text{d}V}\ when\ P=40\$  

•  $-\frac{9}{4}$  

•  $-\frac{4}{9}$  

• Answer option 3

  - $-\frac{8}{5}$  

•  $\frac{9}{4}$  

 $differentiate\ with\ respect\ to\ x:\ \frac{\text{d}}{\text{d}x}\left(2x^3+7\right)^6$  

•  $6x^2\left(2x^3+7\right)^5$  

•  $36x^2\left(2x^2+7\right)^5$  

•  $36x\left(2x^3+7\right)^{5^{ }}$  

•  $36x^2\left(2x^3+7\right)^5$  

calculate the coordinates of the points on the curve  $\sqrt{x^2-4x+8}$  at which  $\frac{\text{d}y}{\text{d}x}=0$  

• (2,3)

• (2,2)

• (2,1)

• (3,2)

 $\ \ \ \ \ Differentiate\ with\ respect\ to\ x:\ \left(x+7\right)^{10}\left(x^2+2\right)^7$  

•  $2\left(x+7\right)^9\left(x^2+2\right)^6\left(12x^2+49x+10\right)$  

•  $2\left(x+7\right)^8\left(x^2+2\right)^5\left(12x^2+49x+10\right)$  

•  $2\left(x+7\right)^{10}\left(x^2+2\right)^6\left(24x^2+49x+10\right)$  

•  $6\left(x+7\right)^9\left(x^{ }+2\right)^6\left(12x^2+49x+10\right)$  

 $Differentiate\ with\ respect\ to\ x:\ \ \frac{\text{d}}{\text{d}x}\left(\frac{2x+5}{3x-4}\right)$ 

•  $-\frac{23}{\left(3x-4\right)^3}$  

•  $-\frac{32}{\left(3x-4\right)^2}$  

•  $\frac{23}{\left(3x-4\right)^2}$  

•  $-\frac{23}{\left(3x-4\right)^2}$  

 $If\ v=t^3+2t^2+3t+1,\ calculate\ the\ value\ of\ \frac{\text{d}^2v}{\text{d}t^2}\ \ \ when\ t=\frac{2}{3}$  

•  $\frac{\text{d}^2v}{\text{d}t^2}=100$  

•  $\frac{\text{d}^2v}{\text{d}t^2}=-20$  

•  $\frac{\text{d}^2v}{\text{d}t^2}=-10$  

•  $\frac{\text{d}^2v}{\text{d}t^2}=10$  
  

if  $y=ax^{\frac{5}{4}},\$ 

where a is a constant , find the approximate percentage change in x when there is a 5% change in y.

• 4%

• 5%

• -4%

• 6%