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No. What you wrote above doesn't mean what you think.Sebastian B said:I unfortunately keep on getting the wrong answer to this problem.
I am supposed to find: dw/dy(1/(w^2+x^2)+1/(w^2+y^2))
Sebastian B said:I attached a picture of how I tried to solve it. Help would be much appreciated.
You mean that you need to find ∂w/∂y given that (1/(w2+x2)+1/(w2+y2)) = 1. Right ?Sebastian B said:I unfortunately keep on getting the wrong answer to this problem.
I am supposed to find: dw/dy(1/(w^2+x^2)+1/(w^2+y^2))
Hello Sebastian B. Welcome to PF !I attached a picture of how I tried to solve it. Help would be much appreciated.
Mark44 said:No. What you wrote above doesn't mean what you think.
I believe what you are supposed to do is use implicit differentiation to find ##\frac{\partial w}{\partial y}##, although that is not clear from what you wrote on the first line. On the third line you have a mistake. Since ##\frac{1}{w^2 + x^2}## does not involve y, its partial derivative with respect to y is zero.
Implicit differentiation is a mathematical technique used to find the derivative of an equation that cannot be easily solved for one variable. It allows us to find the rate of change of a function with respect to one of its variables, even if the function is not explicitly written in terms of that variable.
Implicit differentiation is used when the equation of a curve or surface cannot be easily solved for one of its variables. This commonly occurs when the equation contains both the dependent and independent variables together, making it difficult to isolate the dependent variable.
To perform implicit differentiation, we treat the dependent variable as a function of the independent variable and use the chain rule to differentiate it with respect to the independent variable. Then, we solve for the derivative by collecting terms with the dependent variable on one side and all other terms on the other side.
One advantage of implicit differentiation is that it can be used to find the derivative of a function without needing to explicitly solve for one of its variables. This can be helpful when the equation is difficult or impossible to solve explicitly. It also allows us to find the derivative of implicit functions, which cannot be expressed in terms of a single equation.
Implicit differentiation can only be used to find the derivative of a function with respect to one variable. If we want to find the derivative with respect to multiple variables, we would need to use partial differentiation. Additionally, implicit differentiation may not always yield an explicit formula for the derivative, so it may not be useful in all situations.