Use implicit differentiation to find the slope of the tangent line to the curve 4x^2+4xy+3y^2=27

at the point (2,1)

m=?

Question

Use implicit differentiation to find the slope of the tangent line to the curve 4x^2+4xy+3y^2=27

at the point (2,1) 

m=?

amistre64 · Answer

power, product, power, constant rules

amistre64 · Answer

treat each variable as a function in its own right

anonymous · Answer

I got this so far not sure if it's right 

y'(x)= -x-2y/2x+3y

amistre64 · Answer

4x^2+4xy+3y^2=27

8xx' + 4x'y + 4xy' + 6yy' = 0 ; x'=1

8x + 4y + y'(4x + 6y) = 0

y' = -8x+4y
       -------
         4x+6y

amistre64 · Answer

i wouldnt worry bout simplifyiing; just insert the x and y and then work the numbers

amistre64 · Answer

and i missed a - :)

amistre64 · Answer

maybe a -4x on yours would be better since you simplified;  8x halves to 4x

anonymous · Answer

Oh ok thanks for the help!

amistre64 · Answer

yw

anonymous · Answer

oh what do you mean when u said 'a' ? sorry

amistre64 · Answer

i meant that i missed this negative; had it as a +
            v
y' = -8x-4y
       -------
         4x+6y

anonymous · Answer

Oh ok I see thanks Manh u really help me!