Solve Implicit Functions: dy/dx of y^2+2y=x^3+3x-1

In summary, to find dy/dx of y^2+2y = x^3+3x-1, you can differentiate both sides using the chain rule and simplifying the resulting expression to get dy/dx = 3x^2 + 3 + 1/y^2 * dy/dx. This approach avoids dealing with corner cases and simplifies the resulting expression.
  • #1
madmike159
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Homework Statement



Find dy/dx of y^2+2y = x^3+3x-1

Homework Equations





The Attempt at a Solution



I devided both sides by y so i got y+2 = x^3+3x-1/y
then differentiating i got dy/dx = 3x^2 +3 / dy/dx

I don't think this is right
thanks for any help
 
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  • #2
What you should have gotten was

dy/dx = 3x2 + 3 + 1/y2*dy/dx

As when you differentiate 1/y with respect to x, by the chain rule you get 1/y2*dy/dx To avoid y's in the denominator, it's probably better to start by differentiating rather than dividing both sides by y (you also put off corner cases where y=0 to be dealt with later... and procrastination is always good)
 
  • #3
ty:biggrin:
 

FAQ: Solve Implicit Functions: dy/dx of y^2+2y=x^3+3x-1

What is the process for solving implicit functions?

Solving implicit functions involves finding the derivative of both sides of an equation and then solving for the unknown variable. In this case, we need to find the derivative of y^2+2y and x^3+3x-1 with respect to x.

How do you find the derivative of y^2+2y?

To find the derivative of y^2+2y, we use the power rule, which states that the derivative of x^n is equal to nx^(n-1). In this case, the derivative of y^2+2y would be 2y+2.

How do you find the derivative of x^3+3x-1?

To find the derivative of x^3+3x-1, we use the power rule again. The derivative of x^3 would be 3x^2 and the derivative of 3x would be 3. The derivative of a constant, in this case -1, is 0. So the overall derivative would be 3x^2+3.

What is the next step after finding the derivatives?

After finding the derivatives, we set them equal to each other and solve for the unknown variable. In this case, we would set 2y+2 = 3x^2+3 and solve for y.

Can you provide an example of solving this implicit function?

Yes, for example, if we have the equation y^2+2y=x^3+3x-1, we would first find the derivatives of both sides: 2y+2 and 3x^2+3. Then, we would set them equal to each other and solve for y: 2y+2 = 3x^2+3, 2y = 3x^2+1, y = (3x^2+1)/2. Therefore, the solution to this implicit function is y = (3x^2+1)/2.

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