Question

Find d^2y/dx^2 in terms of x and y for y^2 = 4x

Answer 1

\(y^2 = 4x\)

Let us find out first derivative wrt to \(x\):

\[2y \cdot \frac{dy}{dx} = 4 \cdot 1 \implies 2y \cdot \frac{dy}{dx} = 4 \implies y \frac{dy}{dx} = 2\]

Getting this?

Answer 2

So then the result is 2 ??

Answer 3

We have not found second derivative.. :P

Answer 4

\[y \frac{d^2y}{dx^2} + \frac{dy}{dx} \cdot (\frac{dy}{dx}) = 0 \implies y \frac{d^2y}{dx^2} = - (\frac{dy}{dx})^2 \color{blue}{ \implies \frac{d^2y}{dx^2} = -\frac{1}{y} \cdot (\frac{dy}{dx})^2}\]

Answer 5

Mmm. how did you get 1/y ??

Answer 6

Dividing both the sides by \(y\)..

Answer 7

\(y\) on left hand side will cancel when we divide by \(y\) and right hand side, we will get : \[\frac{1}{y}\]

Answer 8

ohhhh so is −1y⋅(dydx)^2
the final answer?

Answer 9

-1/y * dy/dx the final result ???

Answer 10

(dy/dx)^2 ??

Answer 11

(-1/y) * (dy/dx)^2

Answer 12

ok thank you for the help