x^2+2y^2-11=0 find dy/dx using differentiating implicity
To find dy/dx using implicit differentiation, follow these steps:
1. Start by differentiating both sides of the equation with respect to x. Treat y as a function of x and use the chain rule when differentiating y terms.
d/dx (x^2 + 2y^2 - 11) = d/dx (0)
2. Differentiate each term separately:
d/dx (x^2) + d/dx (2y^2) - d/dx (11) = 0
3. Apply the power rule for differentiation:
2x + 4y * (dy/dx) - 0 = 0
4. Simplify and isolate the dy/dx term:
2x + 4y * (dy/dx) = 0
5. Finally, solve for dy/dx by dividing both sides by 4y:
dy/dx = -2x / (4y)
So, the derivative dy/dx is equal to -2x / (4y) or simply -x / (2y).