Question

Use implicit differentiation to find the derivative dy/dxFind the slope of the curve at the given point. x²y+2y=7 ;(5,1)

Answer 1

To find the derivative dy/dx using implicit differentiation, apply the chain rule and differentiate each term with respect to x. Solve for dy/dx.

Step-by-step explanation:

To find the derivative dy/dx using implicit differentiation, we will apply the chain rule. Let's differentiate each term with respect to x. Starting with x²y, we get 2xy + x²(dy/dx). For 2y, the derivative is 2(dy/dx). And for 7, the derivative is 0. Combining these derivatives, we have 2xy + x²(dy/dx) + 2(dy/dx) = 0. Solving for dy/dx, we get dy/dx = -2xy / (x² + 2).