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

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Answer 1 · 2017-10-07T06:42:51

#dy/dx=2/y#

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#