Higher order derivatives:

Let y = f(x)

First derivative 

Second derivative 

Third derivative  etc.

Example: Find out the 2^nd derivative of ax³ + bx² + cx + d.

Solution : Let y = ax³ + bx² + cx + d.

The Logarithmic Differentiation

If u and v are the functions of independent variable x then to differentiate functions like u^v , first we take log and then differentiate.

Example:    Differentiate  with respect to sin( m cos^{- 1}x).

Solution:        Let y = (log x)^{tan x}  and z = sin(m cos^{- 1}x)

                        So logy = tanx log log x

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