Find dy/dx by using implicit differentiation: x^5+8x^3y^2=20

Question

Find dy/dx by using implicit differentiation: x⁵+8x³y²=20

I got dy/dx= -5x⁴-8x³-24x²y² / 2y.

I was wondering if that was right

Answer 1

Harveer,

Your answer does not look quite right to me.

The first step would look something like this:

5x⁴ +8x³(2yy') +y²(24x²) = 0

From there I get:

16x³yy' = -5x⁴-24x²y²

Now divide both sides by 16x³y to isolate y' (dy/dx).

Based on the above, can you see where you might have gone wrong?