Summary Differentiation

A function f(x) is said to be derivable at a point x = a if A function f(x) is said to be derivable at a point x = a if

Left hand derivative Lf '(a)

Right hand derivative Rf '(a)

f^'(a) exists at x = a iff Lf^' (a) = Rf^'(a)

Working Rules to find derivatives

Derivability implies continuity

Derivative of a constant function is zero.

Logarithmic Differentiation

is obtained by taking log on both sides and then differentiating both sides.

Differentiation of functions expressed in parametric form. If x = x(t) and y = y(t) then 

Working rules for Implicit Differentiation

Step 1:

Step 2:

Differentiate the terms containing x, y or both xy with respect to x.

While differentiating the terms containing y or power of y, first differentiate with respect to y, then multiply by .

Step 3:

Step 4:

If y = f(x) is differentiable then  is called the first order derivative of y = f(x) if is further differentiable the  is called the second order derivative of f(x).Derivatives of standard functions