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 = e6x cos 3x


We have to find


As,


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



Let u = e6x and v = cos 3x


As, y = uv


Using product rule of differentiation:




[ ]


Again differentiating w.r.t x:




Again using the product rule :





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