Question

whats the difference between implicit and explicit differentiation

Answer 1

@mathmale

Answer 2

When you first start out learning differentiation, you find the derivative of a function labeled "y" or "f(x)." That's explicit differentiation; the function has already been solved for "y" or "f(x)."

suppose, however, you had a relationship such as xy^2-5x=4y.

While you could solve this for y, it'd be easier to apply "implicit differentiation," which does not require that you first solve for y.

Apply the derivative operator (d/dx) to all 3 terms of this relationship. Remember that we assume that y is a function of x; this is what is meant by "implicit function."