How to check implicit differentiation results with calculator?

[ktpr2]

What would be the best way to check the result of implicit differentiation with a TI calculator?

 

[DoubleMike]

Pick a random dy/dx and random y.
Then solve for x and see if f(x) = y in the original equation.

 

[M98Ranger]

There are a few different ways to check the result of implicit differentiation using a TI calculator. One option is to graph both the original function and the derivative obtained through implicit differentiation and compare the two graphs. If they overlap or are very similar, then it is likely that the result is correct.

Another way to check the result is to use the calculator's numerical derivative function. This function can be found by pressing the "MATH" button and scrolling to the "nDeriv" option. Input the original function and the value of x for which you want to find the derivative, and then compare the result to the derivative obtained through implicit differentiation. If they are close, then the result is likely correct.

Lastly, you can also manually calculate the derivative using the calculator's differentiation feature. This can be found by pressing the "MATH" button and scrolling to the "dy/dx" option. Input the original function and the value of x for which you want to find the derivative, and then compare the result to the derivative obtained through implicit differentiation. Again, if they are close, then the result is likely correct.

In summary, the best way to check the result of implicit differentiation with a TI calculator is to graph the original function and the derivative, use the numerical derivative function, or manually calculate the derivative using the calculator's differentiation feature. By comparing these results, you can ensure that the result of implicit differentiation is accurate.