Thread: equation of the tangent line?

the question is
find the equation of the tangent line to the curve 2x^3 + 2y^3 = 9xy when x=1, y=2


i tried
d2x^3/dx + d2y^3/dx = d9xy/dx

d2x^3/dx = 6x^2
d2y^3/dx = 6y^2
d9xy/dx = ?

i don't know how to do
how do i do this problem?

Originally Posted by haebinpark

the question is
find the equation of the tangent line to the curve 2x^3 + 2y^3 = 9xy when x=1, y=2


i tried
d2x^3/dx + d2y^3/dx = d9xy/dx

d2x^3/dx = 6x^2
d2y^3/dx = 6y^2
d9xy/dx = ?

i don't know how to do
how do i do this problem?

Use implicit differentiation. The RHS will require the product rule.



Looking at the RHS:







The LHS is simpler:



Set both sides equal to each other and isolate dy/dx. You can then sub in the value you know to find the gradient of the tangent

Spoiler:

A factor of 3 will also cancel out:

but
you have dy/dx on both side?

anyone...?

Originally Posted by e^(i*pi)

Use implicit differentiation. The RHS will require the product rule.



Looking at the RHS:







The LHS is simpler:



Set both sides equal to each other and isolate dy/dx. You can then sub in the value you know to find the gradient of the tangent

Spoiler:

A factor of 3 will also cancel out:

can i go

from 6x^2 + 6y^2 dy/dx = 9y+9x dy/dx

to 6y^2 dy/dx - 9x dy/dx = 9y - 6x^2 ?


and after finding dy/dx
how do i find the equation?
because that was the question... hmm