1irishman said:Homework Statement
2x^3 - 8xy + y^2 = 1
Homework Equations
The Attempt at a Solution
d2x^3/dx - d8xy/dx + dy^2/dx = d1/dx
6x^2 -8(y) + dy/dx(-8x) + 2y(dy/dx) = 0
6x^2 - 8y -8x(dy/dx) + 2y(dy/dx) = 0 I am stuck and can't seem to go further. Someone help?
[/Qdy/dx = 8y-6x^2/2y-8x=4y-3x^2/y-4x
okay got it thank you. i skipped a couple of steps
UOTE]
Differentiating using implicit means finding the derivative of a function that is defined implicitly, rather than explicitly. This means that the function is not in the form of y = f(x), but rather in the form of an equation where both the independent and dependent variables are present.
Explicit differentiation involves finding the derivative of a function that is defined explicitly, in the form of y = f(x). Implicit differentiation involves finding the derivative of a function that is defined implicitly, where both the independent and dependent variables are present in the equation.
The steps for implicit differentiation include differentiating both sides of the equation with respect to the independent variable, using the chain rule when necessary, and isolating the derivative on one side of the equation.
Implicit differentiation should be used when the function is defined implicitly and cannot be easily rewritten in the form of y = f(x). This is often the case with equations involving multiple variables or when the dependent variable is not explicitly defined.
Yes, implicit differentiation can be used on any type of function, as long as it is defined implicitly. However, it can be more complex and time-consuming compared to explicit differentiation, so it may not always be the preferred method.