
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

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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 $\displaystyle dy$ ?

Re: Differentials?
Your response was very helpful indeed.