Question

using implicit differentiation, find the derivative of x^2y + 3xy^3 - x = 3?

Answer 1

just use normal differentiation :) theres no difference

Answer 2

\[x^2y + 3xy^3 - x = 3\]
\[\frac{d(x^2y)}{dx} + \frac{d(3xy^3)}{dx} - \frac{d(x)}{dx} = \frac{d(3)}{dx}\]

Answer 3

the first term uses the product rule; the second term uses it as well the third is and last are simple enough

Answer 4

Thanks for the help. We are required to do it by implicit differentiation is the reason I ask. :)

Answer 5

implicit simply means that the y variable cannot be factored out and solved for;

the rules for their derivates is the exact same procedures

Answer 6

\[Dx(x^2y) = Dx(x^2)y + x^2Dx(y)\]

Answer 7

\[Dx(3xy^3)=Dx(3x)y^3+3xDx(y^3)\]

Answer 8

Kind of making sense now.

Answer 9

Thank you.

Answer 10

youre welcome :)
dont the the variable throw you; the rules for derivatives doesnt care what the variable is

power rule is power rule; chain rule is chain rule; product rule is product rune .... etc