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I don't know how to do implicit differentiation.....

Acceleration is a 2nd derivative (with respect to t)

Yep I know that but i was not able to differentiate it correctly, would you mind checking my work?

Yes, sure....

oh, lets hold a sec and re-write the function better....

\(\large\color{black}{ \displaystyle x(t)=\frac{-b}{2a}+\frac{1}{2a}\cdot\sqrt{b^2+4at} }\)

kind of like that, if it makes sense to you.
(we can do a u-sub, if it is too messy for you)

oh, i frgot ththe chain

Yep I am getting it.

@SolomonZelman but can you check what i did and confirm if it is correct?

oh, sure.. let me look back..

yah that seems better than my way

((and your v is your velocity))
now, a second deriv. is going to be accelearation.

Differentiate the equation on both sides wrt dt which will give
\(\sf 1 = 2axv + bv\)

wrt?

with respect?

wrt = with respect to time

Ok but I did the same and got
1 = axv + bv

wait, you are saying that you got this for the 2nd deriv. or what ?

For first derivative I got 1 = axv + bv but the book says 1=2axv + bv. How?

oh, the power of 2 by x²

t=ax²+bx
(d/dt) t= (d/dt) ax+ (d/dt) bx
(dt/dt)= 2 (dx/dt) ax²⁻¹ + (dx/dt) b

Want an implicit differention example, real quick?

Yes, I think that's my problem. I don't know how to such problems.

Yes I know basics.

yeah, so i will do example or 2-3....

ok

the important part is the chain rule of y' note.
(take you time)

ok, so what is y'?

So basically y' is f'(x)

\(\sf \Rightarrow 1 = 2axV + bV)\)

yes

why do you have .a on the left side? and with respect to what are you differentiating?

With time

dv/dt = a (acceleration)

The constant a on the right hand side is different..

Hehe, I think that's correct.

A is the acceleration

Ummm.. I have four options
2av^2
2av^3
2abv^3
2b^2v^3

Which means i need to find the value in terms of v (velocity)

yeah...

but I got negative same thing...

Yes that's correct. In option it's positive because they are asking Retarding force.

Thanks for bearing with me c:

Lel, thank you for time and help, you were life saver today ;)

Okay... good luck