1. Implicit differentiation

I just started implicit differentiation but something just confused me, maybe perhaps because I have had an incredibly long day and I am tired.

The question is to find the equation of a tangent line, I am fine with the part. the curve is y^5 + x^2y -2x^2 = -1 and the point is (sqrt2, 1)

okay, so I know to differentiate both sides. what I need help with is it differentiates to

5y^4[dy/dx] + 2xy + x^2[dy/dx] - 4x = 0

now I know the final result is dy/dx = [2sqrt2]/7

the part confusing me is in the earlier examples [dy/dx] would be placed next to the y variable like x/2 + 2y[dy/dx] = 0 which yields dy/dx = - x/4y.

Can someone explain the placement of [dy/dx] in my example above. I feel like I probably know the answer but like I said it was an incredibly long day. Thank you!

3. Re: Implicit differentiation

at first I didn't realize what you meant by w r t x, haha

okay I understand.

y^5 is differentiate y wrtx and using the product rule for x^2y, y is being differentiated in x^2[d/dx]y but not in d/dx[x^2] * y