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!