Answer :

Basic Idea: Second order derivative is nothing but derivative of derivative i.e.

√The idea of chain rule of differentiation: If f is any real-valued function which is the composition of two functions u and v, i.e. f = v(u(x)). For the sake of simplicity just assume t = u(x)

Then f = v(t). By chain rule, we can write the derivative of f w.r.t to x as:

√Product rule of differentiation-

Apart from these remember the derivatives of some important functions like exponential, logarithmic, trigonometric etc..

Let’s solve now:

Given, y = log ( log x )

We have to find


So lets first find dy/dx and differentiate it again.

Let y = log t and t = log x

Using chain rule of differentiation:

[ log x) = ]

Again differentiating w.r.t x:


Where u = and v =

using product rule of differentiation:

[ use chain rule to find ]

[ ]

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