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4 years ago

6

If 3x^2+2xy+y^2=2 then the value of dy/dx at x=1 is

1 answer:

Marina CMI [18]4 years ago

6 0

We have that
3x²+2xy+y²<span>=2
</span>
find the derivative-------> <span>(Implicit differentiation)
</span><span>6x+2xdy/dx+2y+2ydy/dx=0
</span>collect dy/dx terms along one side
<span>dy/dx(2x+2y)= -6x-2y </span>
<span>dy/dx= -2(3x+y)/2(x+y) = - (3x+y)/(x+y)
</span>
for x=1
<span>dy/dx= -(3+y)/(1+y)= -(y+3)/(y+1)
</span>
the answer is
dy/dx=-(y+3)/(y+1)

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