Implicit Differentiation: Solving for y' in y^2sin(x)

In summary, to differentiate using implicit differentiation for y^2sin(x), you need to use the product rule first and the final expression will be 2yy'sin(x)+y^2cosx. Make sure to carefully identify the different rules needed for the given function.
  • #1
JessicaJ283782
41
0

Homework Statement



Differentiate using implicit differentiation y^2sin(x)




Homework Equations




I know you need the chain rule and the product rule to solve this


The Attempt at a Solution



So, it would be:

2yy' + y^2cos(x)

Is that correct?
 
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  • #2
JessicaJ283782 said:

Homework Statement



Differentiate using implicit differentiation y^2sin(x)




Homework Equations




I know you need the chain rule and the product rule to solve this


The Attempt at a Solution



So, it would be:

2yy' + y^2cos(x)

Is that correct?
No. Your expression is a product, so you need to use the product rule first.

d/dx(y2sin(x)) = ?
 
  • #3
Mark44 said:
No. Your expression is a product, so you need to use the product rule first.

d/dx(y2sin(x)) = ?


Oops! It should have been 2yy'sin(x)+y^2cosx
 
  • #4
That is correct.
 
  • #5
emlekarc said:
Oops! It should have been 2yy'sin(x)+y^2cosx

Are you guys in the same class or something?
 
  • #6
Lolz. I barely noticed that they're two different people.
 

1. What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function that is not expressed in the form of y = f(x). It is usually used for finding the slope of a curve or the rate of change of a function at a specific point.

2. How is implicit differentiation different from explicit differentiation?

Explicit differentiation involves finding the derivative of a function that is expressed in the form of y = f(x), while implicit differentiation deals with finding the derivative of a function that is not in this form.

3. When is implicit differentiation used?

Implicit differentiation is used when a function cannot be easily solved for y in terms of x, or when a function has multiple variables and is not explicitly written in terms of one variable.

4. What is the process of implicit differentiation?

To use implicit differentiation, the first step is to differentiate both sides of the equation with respect to x. Then, use the chain rule to differentiate any terms that involve y. Finally, solve for dy/dx to find the derivative of the function.

5. What are some real-life applications of implicit differentiation?

Implicit differentiation is used in fields such as physics, engineering, and economics to find the rate of change of various quantities, such as velocity, acceleration, and cost functions. It is also used in curve fitting and optimization problems.

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