If y = x3 log x, prove that 
.
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:
As we have to prove : 
We notice a third order derivative in the expression to be proved so first take the step to find the third order derivative.
Given, y = x3 log x
Let’s find - 
As 
So lets first find dy/dx and differentiate it again.
∴ 
differentiating using product rule:
[
log x) = 
]
Again differentiating using product rule:
[
log x) = 
]
Again differentiating using product rule:
[
log x) = 
]
Again differentiating w.r.t x :
