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Mathematics 68 Online
OpenStudy (anonymous):

Find the equation of the tangent line: yx^2+xy^2=6, (1, 2). Can anyone explain the steps of implicit differentiation?

OpenStudy (anonymous):

y'x^2+y(2x)+x(2yy')+y^2=0

OpenStudy (anonymous):

Thats the first step right?

OpenStudy (anonymous):

y'(x^2+2xy)=-(2xy+y^2) y'=-y(2x+y)/x(x+2y)

OpenStudy (anonymous):

m=y'(at (1,2))=-6/5

OpenStudy (anonymous):

tangent line is y-2=-6/5(x-1)

OpenStudy (anonymous):

On the key it says the slope is -8/5

OpenStudy (anonymous):

oh mistake in computations

OpenStudy (anonymous):

-8/5 is the right ans

OpenStudy (anonymous):

So implicit differentiation, can you quickly verbally go through it, what steps do you do?

OpenStudy (anonymous):

for yx^2 use product rule (derivative of y)x^2+(derivative of x^2) y

OpenStudy (anonymous):

y'x^2+2xy....clear?

OpenStudy (anonymous):

similar for the second term

OpenStudy (anonymous):

OHHHHH!!!! I SEEEEEEE!!!!

OpenStudy (anonymous):

THANK YOU SO MUCH! I really appreciate it :D

OpenStudy (anonymous):

u welcome:)

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