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Find the second order derivatives of the functions given in Exercises 1 to 10. x ^3 log x

 Q5  Find the second order derivatives of the functions given in Exercises 1 to 10. 

        x ^3 \log x

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Given function is
y=x^3\log x
Now, differentiation w.r.t. x
\frac{dy}{dx}=3x^2.\log x+x^3.\frac{1}{x}= 3x^2.\log x+ x^2
Now, the second-order derivative is
\frac{d^2y}{dx^2}= 6x.\log x+3x^2.\frac{1}{x}+2x=6x.\log x+3x+2x = x(6.\log x+5)
Therefore, the second-order derivative is \frac{d^2y}{dx^2} = x(6.\log x+5)

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