can someone explain implicit differentiation to me like d/dx

Question

anonymous · Answer

What do you need with? do you have examples?

anonymous · Answer

y= 4/x find the derivative using d/dx

turingtest · Answer

Example:$$6=y^2x+3y+4x^2$$if we differentiate this implicitly we get$$0=2y(dy/dx)x+y^2+3(dy/dx)+8x$$notice that we used the chain rule on y as a function of x, which gives us dy/dx in our equation. We can therefor solve for dy/dx:
$$dy/dx={-(8x+y^2) \over 2yx+3}$$

turingtest · Answer

Note: the above was differentiated with respect to x (d/dx) as you requested. however you can also differentiate the other way with respect to y (d/dy) like so:
$$6=y^2x+3y+4x^2$$$$0=2yx+y^2(dx/dy)+3+8x(dx/dy)$$notice that now you could solve for dx/dy if you wanted to.

anonymous · Answer

so to differentiate we set the equation equal to zero? thats the part i am confused about how to differentiate

turingtest · Answer

well if you can't differentiate something like 
y=x^5+3x 
then implicit differentiation is still a bit down the road for you.

your equation
$$y= 4/x$$does not require implicit differentiation. is can be solve with the power rule
$${d \over dx}(x^n)=nx^{n-1}$$just notice you can write your equation as
$$y=4x^{-1}$$apply the above formula and tell me what you get

anonymous · Answer

okay using dy/dx it would be 5x^4+3

turingtest · Answer

yes, very good, so what about your problem?$$y= {4\over x}=4x^{-1}$$

anonymous · Answer

-4/x^2?

turingtest · Answer

bingo! 
as you see no implicit differentiation here. good job:)

anonymous · Answer

so can you tell me i an equation does require me to do implicit differentiation?

anonymous · Answer

when*