- #1
flyingpig
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Homework Statement
I tried using D[x = y - y^2, x, NonConstants -> {y}] and it keeps telling me that y - y^2 is not a valid variable.
flyingpig said:I tried again using
D[x = y[x] - y[x]^2, x, NonConstants -> {y}]
And it says
$RecursionLimit::reclim: Recursion depth of 256 exceeded. >>
Further output of $RecursionLimit::reclim will be suppressed during this calculation. >>
flyingpig said:Argh still not working, it's giving me
1 == D[y[x], x, NonConstants -> {y}] -
2 D[y[x], x, NonConstants -> {y}] y[x]
flyingpig said:I am trying to differentiate [tex]x = y - y^2[/tex]
flyingpig said:I am trying to differentiate [tex]x = y - y^2[/tex]
Implicit differentiation is a technique used in calculus to find the derivative of a function that is not explicitly written in terms of its independent variable. This is useful because it allows us to find the rate of change of a function even when it is not in the standard form of y = f(x). It is particularly helpful in solving equations involving multiple variables.
Mathematica uses the standard rules of calculus to perform implicit differentiation. It automatically recognizes that a function is implicitly defined and applies the chain rule and product rule as needed to find the derivative.
Yes, Mathematica can handle implicit differentiation of functions with multiple variables. It can differentiate with respect to any of the independent variables and can also handle partial derivatives.
One common mistake is forgetting to include the necessary syntax for implicit differentiation, such as using the double square brackets [[ ]] around the function. Another mistake is not specifying the variables when using the D function for differentiation.
While Mathematica is a powerful tool for implicit differentiation, it may have difficulty with more complex functions or those involving special functions. It is always important to double-check the results and consider using other methods if necessary.