Can you post the different answers with the respected work?rcurrie said:Help! Keep running this and getting different answers, and none are right.
2xy^8 + 7xy = 27 at the point (3,1)
Answers to what question? There is no question or problem here!rcurrie said:Help! Keep running this and getting different answers, and none are right.
2xy^8 + 7xy = 27 at the point (3,1)
The thread title mentions implicit differentiation. So, differentiate implicitly: $$2y^8 + 16xy^7y' + 7y + 7xy' = 0.$$ At the point $(3,1)$ that becomes $2 + 48y' + 7 + 21y' = 0$. so $69y' + 9 = 0$. That gives $y' = -\dfrac3{23}$. Is that the answer you are looking for?rcurrie said:Help! Keep running this and getting different answers, and none are right.
2xy^8 + 7xy = 27 at the point (3,1)
Implicit differentiation is a method used in calculus to find the derivative of a function that is not explicitly expressed in terms of its independent variable. It is commonly used when a function is given in the form of an equation rather than a specific formula.
Explicit differentiation is used to find the derivative of a function that is expressed explicitly in terms of its independent variable. Implicit differentiation, on the other hand, is used when the function is given in the form of an equation and cannot be easily solved for the dependent variable.
Implicit differentiation is typically used when the function is not easily solvable for the dependent variable, or when the function contains both the dependent and independent variables in different forms (e.g. x and y). It is also useful when finding the derivative of inverse functions.
The steps for implicit differentiation are as follows:1. Differentiate both sides of the equation with respect to the independent variable.2. Use the chain rule for any terms containing the dependent variable.3. Solve for the derivative of the dependent variable.
Yes, implicit differentiation can be used to find higher order derivatives. The process is the same as finding the first derivative, but it may require multiple applications of the chain rule and product rule. It is also important to remember to use the notation for higher order derivatives (e.g. y'', y''', etc.) when solving for them.