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Find #dy/dx# (Implicit differentiation)?

I don't think I'm doing this right... If anybody could solve it.
#x^2+xy-sqrt(y)=3#

Thank you!

Answer 1

Paisley Johnson

It is

#2x+y+xdy/dx-1/2*y^(-1/2)*dy/dx=0#

#2x+y+(x-1/(2sqrty))dy/dx=0#

#dy/dx=(2x+y)/[1/(2sqrty)-x]#

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Answer 2

Ezra Adams

To find ( \frac{{dy}}{{dx}} ) using implicit differentiation, follow these steps:

Differentiate both sides of the given equation with respect to ( x ).
Treat ( y ) as a function of ( x ) and use the chain rule where necessary.
Isolate ( \frac{{dy}}{{dx}} ) on one side of the equation.

For example, if you have an equation ( F(x, y) = 0 ), you'd differentiate both sides with respect to ( x ) and solve for ( \frac{{dy}}{{dx}} ) in terms of ( x ) and ( y ).

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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.

Find #dy/dx# (Implicit differentiation)?

I don't think I'm doing this right... If anybody could solve it. #x^2+xy-sqrt(y)=3# Thank you!

I don't think I'm doing this right... If anybody could solve it.
#x^2+xy-sqrt(y)=3#

Thank you!