Question

Differentiate y^2=4ax

Answer 1

do you know the derivative of y^2 w.r.t x?

Answer 2

\[\frac{d}{dy}y^2=2y \\ \frac{d}{dx}y^2=? \text{ assuming } y=y(x)\]

Answer 3

I don't know, I'm new to this. This is my guess:\[y^2=4ax\]\[y=(4ax)^{\frac12}\]\[y=2\sqrt{a}x^{\frac12}\]\[\frac{dy}{dx}=\sqrt{a}x^{\frac{-1}2}\]\[\frac{dy}{dx}=\frac{\sqrt{a}}{\sqrt{x}}\]

Answer 4

I think you have made a little mistake if you are going to use the chain rule

\[y = (4ax)^{\frac{1}{2}}\]

so let

\[u = 4ax~~~then~~~~\frac{du}{dx} = 4a\]

and making the substitution you get

\[y = u^{\frac{1}{2}}~~~then~~~~\frac{dy}{du} = \frac{1}{2} \times u^{-\frac{1}{2}}\]

lastly you need to know

\[\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}\]

make the substitutions and then simplify. Hope it helps.

Answer 5

Y^2=4ax
2yy'=4a
y'=2a/y=2a/sqrt(4ax)=sqrt(a/x)

Answer 6

\[\frac{ dy }{dx }=\sqrt{\frac{ a }{ x }}\]