To find a derivative, you differentiate. The word derive means something else.Mamdoh Abughalion said:Homework Statement
.[/B]
Find dy/dx
Y^x = X^y
Homework Equations
F'( Ln(x)) = 1/x
Lnx^y = yLnx
The Attempt at a Solution
Ln(Y^x) = Ln(X^y)
X • Lny = Y • Lnx , should I derive now or :
Y = X • Lny/Lnx
Y = X • Logxy , then derive?
I know that , but my instructer told me that the second way is too much " dangerous " and may lead to wrong solution .Orodruin said:It does not matter when you differentiate as long as the equality you are differentiating is equivalent to the original one.
dy/dx, or the derivative of a function, represents the rate of change of that function at a specific point. It is important because it allows us to analyze the behavior of a function and make predictions about its future values.
There are several methods for finding dy/dx, including using the power rule, the chain rule, and the product rule. The method you should use depends on the specific function you are working with and the mathematical tools at your disposal.
The best way to determine which method to use is to first understand the properties of the function you are trying to differentiate. For example, if the function is a polynomial, you can use the power rule. If it is a composite function, you will likely need to use the chain rule.
Some common mistakes to avoid when finding dy/dx include forgetting to apply the chain rule, not simplifying the resulting expression, and miscalculating the derivative of a specific term. It is important to carefully follow the mathematical steps and double-check your work to avoid these errors.
It is important to check our answer when finding dy/dx to ensure that we have correctly applied the necessary rules and calculations. Additionally, checking our answer allows us to catch any mistakes that may have been made and make corrections, leading to a more accurate and reliable result.