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x^2 - xy - y^2 = 3
how do i work out dy/dx?
how do i work out dy/dx?
Originally posted by Zurtex
I'm a little confused with the answers above. When differentiating some function of y with respect to x, is it not simply the derivate of the function with respect to y multiplies by the derivative of y with respect to x?
Such that:
[tex]x^2 - xy - y^2 = 3[/tex]
[tex]2x - \left( y + x \frac{dy}{dx} \right) - 2y \frac{dy}{dx} = 0 [/tex]
[tex]2x - y - x \frac{dy}{dx} - 2y \frac{dy}{dx} = 0 [/tex]
[tex]x \frac{dy}{dx} + 2y \frac{dy}{dx} + y - 2x = 0 [/tex]
[tex](x + 2y) \frac{dy}{dx} = 2x - y[/tex]
[tex]\frac{dy}{dx} = \frac{2x - y}{x + 2y}[/tex]
Please say if this is wrong somehow, I need the practise.
I didn't really understand the method though and got a bit confused so I wanted to check I knew how to do it, I was unsure why the example of if xy = 1 was given.Originally posted by HallsofIvy
Yes, that was, in fact, exactly what matt grime orginally said!
Differentiation is a mathematical process used to find the rate of change of a function. To differentiate a function, you need to follow a set of rules based on the type of function you are dealing with.
The three main types of functions that can be differentiated are polynomial functions, exponential functions, and trigonometric functions. Each type requires a different set of rules to differentiate.
No, not all functions can be differentiated. Some functions, such as step functions or absolute value functions, are not continuous and therefore cannot be differentiated.
The purpose of differentiating a function is to find the instantaneous rate of change of the function at a specific point. This can be useful in many applications, such as finding the maximum or minimum value of a function, or determining the velocity of an object at a given time.
One common mistake is to forget to use the chain rule when differentiating composite functions. Another mistake is to forget to apply the product rule when differentiating a product of two functions. It is important to carefully follow the rules and double check your work when differentiating a function.