Question

How do you find `(dy)/(dx)` given `y^2=4x`?

Answer 1

`dy/dx=2/y`

Explanation:

The equation is `y^2=4x`

When we differentiate the equation with respect to `x` we will apply the chain rule on the LHS.

`d/dxy^2=d/dx4x`

`2yd/dxy=4`

`2ydy/dx=4`

`dy/dx=2/y`

Here we know `y` is a variable, therefore we applied the chain rule.

If you want to check your answer ->

We found out that `dy/dx=2/y`

Now we will convert it into a differential equation

`ydy=2dx`

When we integrate (take the antiderivative) both the sides we get

`y^2/2=2x`

That is same as the equation we started out with
i.e, `y^2=4x`