If y is a function of u, u is a function of v and v is a function of x. Then, dy / dx = dy / du * du / dv * dv / dx.
2. Differentiation Using Substitution In order to find differential coefficients of complicated expression involving inverse trigonometric functions some substitutions are very helpful, which are listed below.
3. Differentiation of Implicit Functions
If f( x, y) = 0, differentiate with respect to x and collect the terms containing dy / dx at one side and find dy / dx.
Shortcut for Implicit Functions For Implicit function, put d / dx { f( x, y)} = – ∂f / ∂x / ∂f / ∂y, where ∂f / ∂x is a partial differential of given function with respect to x and ∂f / ∂y means
Partial differential of given function with respect to y. 4. Differentiation of Parametric Functions If x = f( t), y = g( t), where t is parameter, then dy / dx =( dy / dt) /( dx / dt) = d / dt g( t) / d / dt f( t) = g’( t) / f’( t)