# Differentials?

• Aug 4th 2011, 12:16 PM
homeylova223
Differentials?
With the information given compare delta y and dy.

1. y=(x)^3 x=1 delta x= 0.1

dy= f'(x)(dx)

dy= 3(1)(0.1)

dy=.3

delta y= f(x+delta x)- f(x) I am having trouble finding delta y

delta y= (1+.1)-(1) ? Is this what I would do

My second question is similar

2.y= x^4+1 x=-1 and delta x=.01

dy=(-4)(-1)(.01)
dy=.04

But I am having trouble finding delta y
• Aug 4th 2011, 12:41 PM
skeeter
Re: Differentials?
$\displaystyle y = x^3$

$\displaystyle x = 1$ , $\displaystyle \Delta x = 0.1$

$\displaystyle \frac{\Delta y}{\Delta x} = \frac{y(1.1) - y(1)}{1.1 - 1} = \frac{1.1^3 - 1}{1.1 - 1} = \frac{0.331}{0.1}$

therefore ...

$\displaystyle \Delta y = 0.331$

$\displaystyle y = x^3$

$\displaystyle \frac{dy}{dx} = 3x^2$

$\displaystyle dy = 3x^2 \cdot dx$

$\displaystyle dy = 3(1^2) \cdot (0.1) = 0.3$

see the difference between $\displaystyle \Delta y$ and $\displaystyle dy$ ?
• Aug 4th 2011, 12:54 PM
homeylova223
Re: Differentials?