The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Differentiation from first principles

80ABE74F-DAFA-4BB8-854E-23F74A7675E5.jpg.jpeg
I have (h^3+6h^2+7h-2-x^3+5x)/h so far but I’m not sure how to divide all that by h as there are x terms and -2 do I think I’ve done it wrong
Reply 1
Avatar for Sinnoh
Sinnoh
22
You must have made an error with the algebra. I got x3+3x2h+3xh2+h3−5x−5h−x3+5xh\dfrac{x^3 + 3x^2h + 3xh^2 + h^3 - 5x - 5h - x^3 + 5x}{h}. That simplified to 3x2+3xh+h2−53x^2 + 3xh + h^2 - 5 then applying the limit gave 3x2−53x^2 - 5.
Is this 051C0E69-82E1-4942-B595-2BD88B5BF11D.jpg.jpeghow I should have started?
Reply 3
Avatar for Sinnoh
Sinnoh
22
Original post by hollyrose123
Is this 051C0E69-82E1-4942-B595-2BD88B5BF11D.jpg.jpeghow I should have started?


Yeah, although I would keep it in terms of x throughout and then substitute at the end.
Do you mean use x+h?
The only thing you're missing with this equation is consistency. If you're going to sub in x = 2 for f(x+h) for the differentiation by first principles equation (as you have) then you must also subtract f(2) for f(x) (which you have not). Stay consistent, if you sub in x = 2 make sure you do it for both parts, or if you don't then you can use f(x+h) - f(x) into the equation and that would work to find the derivative and then you can sub in x = 2.
Original post by hollyrose123
80ABE74F-DAFA-4BB8-854E-23F74A7675E5.jpg.jpeg
I have (h^3+6h^2+7h-2-x^3+5x)/h so far but I’m not sure how to divide all that by h as there are x terms and -2 do I think I’ve done it wrong


image-c6aef2a7-66a1-4b13-ba36-b2f4fa61a88d1458614747-compressed.jpg.jpeg

maybe this can help :smile:
Original post by Sinnoh
Yeah, although I would keep it in terms of x throughout and then substitute at the end.


ohh...the numerator...instead of -(x^3-5x)...you should replace your value for X so it should be -(2^3-5+2))
Thanks so much that’s what I got :smile:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you