Q7  Find the second order derivatives of the functions given in Exercises 1 to 10. 

       e ^{6x}\cos 3x

 

Answers (1)

Given function is
y= e^{6x}\cos 3x
Now, differentiation w.r.t. x
\frac{dy}{dx}=6e^{6x}.\cos 3x +e^{6x}.(-3\sin 3x)= e^{6x}(6\cos 3x-3\sin 3x)
Now, second order derivative is
\frac{d^2y}{dx^2}= 6e^{6x}(6\cos3x-3\sin3x)+e^{6x}(6.(-3\sin3x)-3.3\cos3x)
          = 6e^{6x}(6\cos3x-3\sin3x)-e^{6x}(18\sin3x+9\cos3x)
          e^{6x}(27\cos3x-36\sin3x) = 9e^{6x}(3\cos3x-4\sin3x)
Therefore,  second order derivative is \frac{dy}{dx} = 9e^{6x}(3\cos3x-4\sin3x)

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