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'.


`(d)/(dx) f(x) = (d)/(dx) g(y) \\ \\ (d)/(dx) f(x) = (d)/(dy) g(y) *(dy)/(dx)`

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


`4x^3 = -csc^2(y) (dy)/(dx) \\ \\ (dy)/(dx) = -4 x^3 sin^2 (y)`