Explicit Differentiation vs Implicit Differentiation
Explicit Differentiation:
As we have discussed before,explicit function when we write y as function of “x”
Example
$$y=x^2$$$$\text{Let}\;y=x^2+sinx$$
Fact:Here there is no y which means that explicit differentiation
$$y’=2x+cosx$$
Implicit Differentiation:
When y cannot be written as function of “x”
Example
$$xy=8$$
$$xy’+y(1)=0$$
$$xy’+y$$
By use of product rule(fg’+gf’)
$$\frac{dy}{dx}=\frac{-y}{x}$$