Question

Find the derivative of (ax^2 + b)^2 , using first principle.

Please :((

Answer 1

i can try to solve it

Answer 2

\[\frac{ d }{ dx }(ax ^{2}+b)^{2}=2(ax ^{2}+b)\frac{ d }{ dx }(ax ^{2}+b)\]

Answer 3

So you have lim h->0 [ (a(x+h)^2 +b)^2 - (ax^2 +b)^2 ]/h

whats is your attempt ?

Answer 4

sorry, i m not using first principle

Answer 5

i m just solving this problem

Answer 6

should i proceed

Answer 7

hmm, nevermind, You;re forgiven! ;)

Answer 8

See .. I know how to solve it generally.. and I even got the answer!

It's just that I want to know how to solve is using the first principle! @shamim ; @shubhamsrg

Answer 9

Surely you must have got the answer, what I asked was, what attempt have you made, in the solution via first principle till now ?

Answer 10

Erm :P I kinda completed the solving ka process, but I didn't get the same answer :P

Answer 11

I see, leme try
lim h->0 [ (a(x+h)^2 +b)^2 - (ax^2 +b)^2 ]/h

lim h->0 [ a(x+h)^2 + b + (ax^2 +b) ] [a(x+h)^2 + b - (ax^2 +b) ]/h

lim h->0 [ a( (x+h)^2 + x^2) +2b ] [a(x+h+x)(x+h-x) ]/h

lim h->0 [a ((x+h)^2 +x^2) +2b] [a(2x+h)(h)]/h

lim h->0 [a ((x+h)^2 +x^2) +2b] [a(2x+h)]

now you may put h=0 in there
you'll get

( a(2x^2) +2b )(2ax)
=>2(ax^2 +b)(2ax)

Did you follow ?