introductory calculas (1 Viewer)

[Teddythebenny]

hi guys

i was wondering if anyone here could help me with the 1st principal rule and how it works ?

i know the short form, but i kinda dont get the forst principle rule of calculas

plz help

 

[jb_nc]

f'(x) = lim_h->0((f(x+h) - f(x)/h)

Say, let f(x) = x². Let's differentiate from Newton's first principle:

f'(x) = ((x+h)² - x²/h)
Expanding (x+h)²
f'(x) = (x² + 2xh + h² - x²)/h)
Subtracting x²
f'(x) = (2xh + h²)/h
Taking out common factor h
f'(x) = h(2x + h)/h
Cancelling h
f'(x)= 2x + h
Now, take the limit as h -> 0
We get,
f(x) = 2x
Which d(x²)/dx = 2x

 

[jb_nc]

Also, learn to spell.

 

[Teddythebenny]

thx for that

i get it now .. although i prefer the short cut ..

thank you

 

[undalay]

they can ask you to differentiate something using first principles, so you will need to know how to do them.

 

[HKHSCstudent]

回覆: Re: introductory calculas

just remember the formulas

 

[Foxodi]

Re: 回覆: Re: introductory calculas

I think my maths teacher said they havent asked for the first principals in the HSC for 20 years or something But still, learn it anyway