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What is 2xy differentiated implicitly?

Answer 1

Evelyn Agard

#y'=(2y)/(1-2x)#

The question does not specify with respect to what so I'll assume y is a function of x.

Use the product rule:

#y' = d((u.v))/dx=v.du/dx+u.dv/dx#

So:

#y'=2x.y'+y2.dx/dx#

#y'=2x.y'+2y#

#y'=(2y)/(1-2x)#

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Answer 2

Elijah Abram

The answer is #=-y/x#

The function is

#f(x,y)=2xy#

The partial derivatives are

#(delf)/(delx)=2y#

#(delf)/(dely)=2x#

Therefore,

#dy/dx=-((delf)/(delx))/((delf)/(dely))=-(2y)/(2x)=-y/x#

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Answer 3

Emilia Aguilar

The implicit differentiation of 2xy is 2y + 2x(dy/dx).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.