Q. 325.0( 2 Votes )
If y = ex cosx, prove that (CBSE 2012)
√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:
y=ex cos x
TO prove :
Clearly from the expression to be proved we can easily observe that we need to just find the second derivative of given function.
Given, y = ex cos x
We have to find
So lets first find dy/dx and differentiate it again.
Let u = ex and v = cos x
As, y = u*v
∴ Using product rule of differentiation:
[ ∵ ]
Again differentiating w.r.t x:
Again using the product rule :
[∵ –sin x = cos (x + π/2)]
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