Find the second order derivatives of each of the following functions:
x3 log x
√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 = x3 log x
We have to find 
As 
So lets first find dy/dx and differentiate it again.
∴ 
Let u = x3 and v = log x
As, y = uv
∴ Using product rule of differentiation:
∴ 
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Again differentiating w.r.t x:
Again using the product rule :
[ ∵ 
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