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
