Implicit differentiation question Given: yx−y=x2+1

William Boggs

William Boggs

Answered

2022-01-22

Implicit differentiation question
Given: yxy=x2+1

Answer & Explanation

Pansdorfp6

Pansdorfp6

Expert

2022-01-22Added 27 answers

yxy=x2+1
You claim that y=2x
so that y=x2+C
This means x2+Cxx2C=x2+1
This is absqrt, since the quotient of two second degree polynomials can't be a second degree polynomial. In fact you get two non vanishing terms x3 and x4 which are off.
I don't understand what your procedure is, also. I would proceed as follows:
yxy=x2+1
ddx(yxy)=ddx(x2+1)
y(xy)(1y)y(xy)2=2x
yxy(xy)2=2x
yx=2x(xy)2+y
y=2(xy)2+yx
Barbara Meeker

Barbara Meeker

Expert

2022-01-23Added 38 answers

An explicit approach:
Rewrite as y=(xy)(x2+1), and factor out y to get y=x3+xx2+2, This is straightforward to differentiate, yielding dydx=x4+5x2+2(x2+2)2.

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