The first thing wrong is starting the line below with =. By putting that = at the start of each line, you are more likely to lose track of the two sides of the equation you started with.domyy said:Homework Statement
Use implicit differentiation to find dy/dx.
Homework Equations
xey - 10x + 3y = 0
The Attempt at a Solution
The more serious mistake is above. You didn't take the derivative of xey correctly. d/dx(xey) = ey + xey*y'. Do you see why?domyy said:= [xey + ey(y)'] - (10x)' + (3y)' = 0
No, I believe their answer is (10 - ey)/(xey + 3). Note the parentheses, and the 3 instead of the 3y that you had.domyy said:= xey + ey(y') - 10 + 3(y') = 0
= y' (ey + 3) = 10 - xey
= y' = 10 - xey/ ey + 3y
However, my book says the answer: 10 - ey/ xey + 3y.
domyy said:What am I doing wrong?
Thanks!
Don't start your work with =.domyy said:About taking the derivative wrongly, my question is: How does that differ from y= xe^x - e^x?
Because I was trying to follow the same thinking when solving the problem in question.
This is how I solved it ( and I got it right):
In this problem,domyy said:= xe^x + e^x (x)' - e^x(x)'
= xe^x + e^x - e^x
= e^x ( x -1 + 1)
= xe^x
Thanks!
Implicit differentiation is a method used in calculus to find the derivative of a function that is defined implicitly, meaning it is not explicitly written in terms of one variable. This is often the case for equations involving multiple variables or complex functions.
Explicit differentiation involves finding the derivative of a function that is written explicitly in terms of one variable. Implicit differentiation, on the other hand, is used for functions that are not explicitly written in terms of one variable and requires the use of the chain rule.
The process for implicit differentiation involves taking the derivative with respect to x on both sides of the equation, using the chain rule when necessary, and isolating dy/dx on one side of the equation. Then, solve for dy/dx to get the derivative of the function.
Implicit differentiation should be used when the function is not explicitly written in terms of one variable, making it difficult or impossible to find the derivative using explicit differentiation. This method is commonly used in physics, engineering, and other fields that involve complex equations.
Some common mistakes to avoid when using implicit differentiation include forgetting to apply the chain rule, not isolating dy/dx, and misplacing negative signs. It is important to carefully follow the steps of implicit differentiation and check your work to avoid these errors.