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 = …..equation 1


As we have to prove : ..


We notice a second-order derivative in the expression to be proved so first take the step to find the second order derivative.


Let’s find


As


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


As y is the product of two functions u and v


Let u = log x and v = 1/x


Using product rule of differentiation:




[ log x) = & ]




Again using the product rule to find :



[ log x) = & ]



….. proved


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