Question

find dx/dy if y=sin2x

Answer 1

y = sin(2x)

If you differentiate sin(x), you get cos(x).

So, if you differentiate sin(u) you will get cos(u).

Then let u = 2x.

Since u = 2x, then du/dx = 2.

And dy/dx = (dy/du)*(du/dx).

Now, y = sin(u), with dy/du = cos(u).

So, dy/dx = (dy/du)*(du/dx) = cos(u)*2

i.e. dy/dx = 2cos(2x)

Answer 2

y=sin2x

dy/dx=2cos2x=2sqrt(1-sin^2(2x))=2sqrt(1-y^2)

Therefore dx/dy=1/(2sqrt(1-y^2))