Solving Derivative dy/dx: y, sin(xy) + 1 = cos x

  • Thread starter skyhawk714
  • Start date
  • Tags
    Derivatives
In summary, the conversation is about finding the derivative of y, dy when e^y*cos(x)=1+sin(xy) by using implicit differentiation. The person initially attempted the problem but got an incorrect answer, and is now asking for guidance on how to solve it correctly.
  • #1
skyhawk714
4
0
1. Find the derivatie of y, dy when e/\(y) cos x=1 + sin (xy)
---
dx

2. I don't know of any Relevant equations


3. The first time i tried the problem i got e/\(y) cos X+ y cos (xy)
------------------------
e/\(y) sin x- x cos (xy)

but i know that's not right...how do i even do a problem like this?
 
Physics news on Phys.org
  • #2
You are trying to use implicit differentiation to find dy/dx given (e^y)*cos(x)=1+sin(xy), right? Your answer has the right sort of general form, but it's not correct. Differentiate both sides of (e^y)*cos(x)=1+sin(xy) using the chain rule and show the steps you did to get your answer.
 
Last edited:

FAQ: Solving Derivative dy/dx: y, sin(xy) + 1 = cos x

What is a derivative?

A derivative is a mathematical concept that measures the rate of change of a function with respect to its independent variable. In other words, it tells us how much a function is changing at a specific point.

How do you solve for dy/dx?

To solve for dy/dx, we need to use the rules of differentiation, such as the power rule and the chain rule. In this case, we would use the chain rule to find the derivative of sin(xy) and the power rule to find the derivative of cos x. We would then set these derivatives equal to each other and solve for dy/dx.

What is the process for solving this specific equation?

The process for solving this equation is to first isolate the term with dy/dx on one side of the equation. We can then use the inverse of the chain rule to solve for dy/dx. We would then substitute the values of x and y into the equation to find the specific value of dy/dx at that point.

Can you provide an example of solving this derivative equation?

Sure, let's say we have the equation y = sin(xy) + 1 = cos x. To solve for dy/dx, we would first rearrange the equation to get sin(xy) = cos x - 1. We would then use the chain rule to find the derivative of sin(xy), which is cos(xy) * (y + xy'). We would also use the power rule to find the derivative of cos x, which is -sin x. We would then set these derivatives equal to each other and solve for dy/dx.

What are the practical applications of solving derivatives?

Solving derivatives is essential in many fields of science and engineering, such as physics, economics, and biology. It allows us to analyze and predict the behavior of various phenomena, such as motion, growth, and change. For example, in physics, derivatives are used to calculate velocity and acceleration, while in economics, they are used to determine the marginal cost and revenue of a product. In biology, derivatives are used to model population growth and determine the rate of change in a species' population over time.

Similar threads

Solve the problem involving the given double integral
Replies
1
Views
915
Find f(x,y) given partial derivative and initial condition
Replies
6
Views
1K
Is My Solution to This Exact Differential Equation Correct?
Replies
6
Views
1K
Line Integral of circle in counterclockwise direction
Replies
5
Views
1K
How should I find the equilibrium points and the general equation?
Replies
3
Views
580
Solve p = P(2X <= Y^2) using double integral
Replies
4
Views
1K
Uniform Continuity of functions
2
Replies
40
Views
760
Question on Two Differentiation Techniques
Replies
25
Views
1K
Find the general solution of this nonlinear ODE: xy' + sin(2y) = x^3*sin^2(y)
Replies
13
Views
2K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top