Let 5x^2 - 3xy + 58 = 2y^3
Use implicit differentiation to find y' for the above equation.
The first thing I did was move 2y^3 over to that everything is equal to 0. With the -3xy I used the product rule and expanded that.
After solving I got....
10x(3 * y + 3x * 1dy/dx)- 6y^2dydx= 0
= 10x-3y+3x*(1*dy/dx)-(6y^2*dydx)=0
Pulled out -6y^2*dy/dx (13x-3x)=0
Moved everything over and got...
-6y^2*dy/dx = 13x+3y
Moved -6y^2 over by dividing and the final answer I got was..
dy/dx = (-13x+3y)/(-6y^2)
Im searching online and its saying that I have the wrong answer.
10 x-3xdy/dx-y(3x)=6y^2 dy/dx
(6y^2+3x)dy/dx = 10 x -3xy
dy/dx = (10x-3xy)/(6y^2+3x)
Just do it term by term the way it stands,
the only one to be careful with is the -3xy, since you have to use a product rule
5x^2 - 3xy + 58 = 2y^3
10x - 3x dy/dx -3y + 0 = 6y^2 dy/dx
10x - 3y = 6y^2 dy/dx + 3x dy/dx
factor out the dy/dx and just flip the equation
dy/dx(6y^2 + 3x) = 10x - 3y
dy/dx = (10x - 3y) / (6y^2 + 3x)
check:
http://www.wolframalpha.com/input/?i=find+dy%2Fdx+for+5x%5E2+-+3xy+%2B+58+%3D+2y%5E3
5x^2 - 3xy + 58 = 2y^3
10x-3y-3xy'=6y^2 y'
y'(6y^2+3x)=10x-3y
y'=(10x-3y)/(6y^2+3x)
check my work.
geepers, we all at at the same time got the same answer.
Nah, I carried an incorrect extra x
THANK YOU!!!!
To find the derivative of y with respect to x (or y'), we can use implicit differentiation. Here's how to solve the equation step by step:
1. Start with the equation: 5x^2 - 3xy + 58 = 2y^3.
2. Rearrange the equation so that all terms are on one side: 5x^2 - 3xy - 2y^3 + 58 = 0.
3. Apply the product rule to the term -3xy. The product rule states that (uv)' = u'v + uv'.
4. Differentiate each term with respect to x, treating y as a function of x.
- The derivative of 5x^2 is 10x.
- For the term -3xy, apply the product rule. The derivative of -3xy is (-3x * y) + (-3y * x) = -3xy - 3yx = -6xy.
- The derivative of -2y^3 is -6y^2 * (dy/dx) using the chain rule.
5. Combine the results and set the expression equal to 0: 10x - 6xy - 6y^2 * (dy/dx) + 58 = 0.
6. Rearrange the equation to isolate the term involving (dy/dx):
-6y^2 * (dy/dx) = -10x + 6xy - 58.
7. Divide both sides of the equation by -6y^2 to solve for (dy/dx):
dy/dx = (-10x + 6xy - 58) / (-6y^2).
So the correct answer is: dy/dx = (-10x + 6xy - 58) / (-6y^2).