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



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


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:

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



