Question

Use implicit differentiation to find . dy/dx a) x3 – xy + y3 = 1

Answer 1

Step-by-step explanation:

We have,

${x}^{3} - xy + {y}^{3} = 1$

Differentiating w.r.t x, we have,

$3 {x}^{2} - y - x \frac{dy}{dx} + 3 {y}^{2} \frac{dy}{dx} = 0$

$\implies(3 {x}^{2} - y) - (x - 3 {y}^{2}) \frac{dy}{dx} = 0$

$\implies \frac{dy}{dx} = \frac{3 {x}^{2} - y }{x - 3 {y}^{2} }$