vikcool812 said:I have a relation xy=c2 , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c2/x , then dy/dx comes out to be -c2/x2 , what's going wrong ?
Nothing since -y/x = -c²/x2 !vikcool812 said:I have a relation xy=c2 , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c2/x , then dy/dx comes out to be -c2/x2 , what's going wrong ?
"2 different dy/dx of xy=c^2" is a mathematical expression that represents the derivative of a function with respect to both x and y variables, where the product of x and y is equal to a constant value (c^2).
The derivative of xy=c^2 can be calculated by using the product rule of differentiation, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. In this case, the derivative would be (x * dy/dx) + (y * dx/dx) = 0, which simplifies to dy/dx = -y/x.
One example of "2 different dy/dx of xy=c^2" is the function y = 4x^2, where the derivative with respect to both x and y would be dy/dx = -4x/y.
"2 different dy/dx of xy=c^2" has various applications in real life, such as in physics, engineering, and economics. It can be used to calculate rates of change, optimize processes, and model relationships between variables.
Yes, it is possible to have more than 2 different dy/dx in "2 different dy/dx of xy=c^2". For example, the function xy^2 = c^2 would have three different derivatives with respect to x, y, and the constant c.