i have a question that i have to do and as im not very good at the calculus part of the course i was wondering if someone could help me. the question is find the derivative of 4x^2 - 3x from first principles. i know what first principles is and i am just dont know how to answer the question. i know how to differentiate is normally but its just the working. any help would be awesome.
You could use the power rule - aX^n = anX^n-1, example the derivative of 2X^3 = 6X^2 Or you could do the horribly long method (f(X+deltaX) - f(X)) / deltaX example of this: X^2 + 7X [(X + deltaX)(X + deltaX) + 7(X + deltaX)] - (X^2 + 7X) (all over deltaX but we don't care about that yet) X^2 + 2XdeltaX + deltaX^2 + 7X + 7deltaX - X^2 - 7X <-- notice in this step all terms that don't have a deltaX will cancel 2XdeltaX + deltaX^2 + 7deltaX <-- remember how this is all divided by deltaX? your dirivitive (well, almost) = 2X + deltaX + 7 Get rid of the last remaining deltaX by taking the limit as deltaX approaches 0 and the derivative is 2X + 7. L J
The definition of the (f(X+deltaX) - f(X)) / deltaX method, which is derivation from first principles, applies as deltaX tends to zero, so as above, just remove all the deltaXs in the equation at the end as they are zero.
does someone just want to use the equation for the question to show me as im still slightly confused mainly by like what Colonel Sanders said under X^2+7X
Trick to be good in Calculus: Calculus I: Practice, practice, and practice. Calculus II: Even more practice. Once you got it, you will be able to do anything that is thrown at you quiet easily.
Made it using Microsoft Equation Editor in Word 2003, would have used Math in OpenOffice but didn't have it installed on that computer. The equation editor in Word 2007 is a lot better than in 2003 though, probably worth it if you do a lot of equation writing.
