pr0blumz said:(8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0
pr0blumz said:(8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0
pr0blumz said:I'm still getting (5y-8x)/(3y-5x)
pr0blumz said:(8x-5y)/(5x-3y)
HallsofIvy said:As rockfreak667 said before, you already had the correct answer:
(5y-8x)/(3y-5x)= (8x-5y)/(5x-3y)
pr0blumz said:I have another problem as well.
x + (sqrtx)(sqrty) = 2y
1 + (x^1/2)/(2y^1/2)y' + (y^1/2)/(2x^1/2) = 2y'
My question is why I suppose to multiply both sides by (2x^1/2 * y^1/2) and not both of the denominators?
Implicit differentiation is a mathematical method used to find the derivative of a function that is not explicitly defined in terms of one variable. It is often used when the function is difficult or impossible to solve for one variable alone.
Implicit differentiation allows us to find the derivative of a function without having to solve for one variable. This can be helpful when dealing with complex functions or when the function is not defined explicitly in terms of one variable.
Explicit differentiation involves finding the derivative of a function that is defined explicitly in terms of one variable. Implicit differentiation, on the other hand, is used when the function is not defined explicitly and involves differentiating both sides of the equation with respect to the variable of interest.
The steps for implicit differentiation are as follows: 1) Differentiate both sides of the equation with respect to the variable of interest, treating the other variables as constants. 2) Simplify the resulting equation by collecting like terms. 3) Solve for the derivative by isolating the variable of interest on one side of the equation.
Implicit differentiation is used in many fields of science and engineering, such as physics, economics, and biology. It can be used to find the rate of change in a system or to optimize a process. For example, it can be used to find the maximum profit for a company or to determine the velocity of an object in motion.