Question

X4=coty find dy/dx by implicit differentiation

Answer 1

For implicit, you take the derivative of entire equation. When it is a function of 'y', you must multiply derivative by ' dy/dx'.

$\frac{d}{dx} f(x) = \frac{d}{dx} g(y) \\ \\ \frac{d}{dx} f(x) = \frac{d}{dy} g(y) *\frac{dy}{dx}$

For this example, f(x) = x^4, g(y) = cot(y)
After differentiating, solve for 'dy/dx':

$4x^3 = -csc^2(y) \frac{dy}{dx} \\ \\ \frac{dy}{dx} = -4 x^3 sin^2 (y)$