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The higher number known equation: e ^ y + e ^ (2x) = XY, find the derivative dy / DX of the implicit function determined by the equation
F (x, y) = e ^ y + e ^ (2x) - xy = 0 using the existence theorem of implicit function:
Dy / DX = - f 'x / F' y, f 'x, f' y are the partial derivatives of F (x, y) to x, y, respectively
f 'x=2e^(2x)-y
f 'y=e^y-x
dy/dx=-[2e^(2x)-y]/(e^y-x)
Of course, you can also take the derivative of X on both sides of e ^ y + e ^ (2x) = XY, and find y ', and the result is the same
What do Dy and DX in higher numbers mean in derivatives and calculus, respectively
Dy, DX are all calculus, dy / DX is the derivative
Dy / DX = 1 / (x + y) find the general solution. The simpler the better
Answer: dy / DX = 1 / (x + y) take the reciprocal on both sides: DX / dy = x + y, take x as a function of Y, then there is: X '- x = y, the characteristic equation of homogeneous equation x' - x = 0 is A-1 = 0, a = 1, so: the general solution of homogeneous equation x '- x = 0 is x = CE ^ x, let the special solution of X' - x = y be x * = my + B, and X * '= m substitute into: m-my-b = y, so: M = - 1, B = - 1
High number: do you want to add C after y for dy / DX integral?
If you're an indefinite integral, you need a constant C. the integral gives a general solution. If you don't add C, it's just a special solution
What does dy / DX mean? In dy / DX, what do D, x, y and the division sign in the middle mean? I hope you can give several examples to illustrate in detail, Thank hikiss1010 for your answer, but I have a few questions to ask What is differential quotient and incremental refinement? Because I am not good at English when studying abroad, I can't understand what the teacher says in class, and no Chinese can help me with my math, so many proper nouns don't know what they mean. I hope you can explain my question again,
I don't know what you're talking about upstairs
Dy / DX can be understood as y deriving from X
It can also be understood as derivative, that is, the derivative of differential
First of all, we should know that y here is a function of X, that is, y = f (x)
Dy is the differential of Y and DX is the differential of X
Is to refine the increment
DX is a very small X
Dy = a · Delta (that is, a triangle) x
Dy is the linear principal part of y that changes due to the change of X
Without a graph, it is not easy to explain the meaning of the word linear principal
That is, Dy is part of delta y
Finally, dy / DX is the linear increment of Y divided by X, so it's exactly the tangent of a curve
The meanings of Y 'and Dy and dy / DX and their differences
Y 'and dy / DX are called derivative or derivative. Y' is the abbreviation of dy / DX, which calculates the derivative of the default independent variable. For example, y = f (T), y 'is dy / dt
Dy is the differential and the limit form of difference. Dy = y'dx
Strictly speaking, dy / DX is not the quotient of Dy and DX, but many operations are similar to quotient. It can generally be regarded as quotient
RELATED INFORMATIONS
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