small increment and approximation

 $\frac{\text{d}y}{\text{d}x}=3x^2\ +1$  

 $\frac{\text{d}y}{\text{d}x}=3x^{ }\ +x$  

 $\frac{\text{d}y}{\text{d}x}=6x^{ }+2$  

 $\frac{\text{d}y}{\text{d}x}=6x^{ }+2-4$  

small changes in y

small changes in x

small changes in axis

big changes in xy

 $\frac{dy}{dx}=30x^6+7$  

 $\frac{dy}{dx}=30x^5+7$  

 $\frac{dy}{dx}=56x^5+7x$  

 $\frac{dy}{dx}=0$  

delta y

delta x

delta dy

alpha y

find delta $y$

find $\partial y$

find new $y$

find $\frac{dy}{dx}$

 $\frac{dy}{dx}=34x$  

 $\frac{dy}{dx}=34$  

 $\frac{dy}{dx}=34+2$  

 $\frac{dy}{dx}=34x^2$  

approtimation

approxemation

aproximation

approximation

0.0002

0.002

0.02

-0.002

 $\delta y$  

 $\text{d}y$  

 $\text{}\frac{dx}{dy}$  

 $\frac{\delta x}{\delta y}$  

15

53

125

115