Question #7454e

1 Answer
Jul 19, 2017

Answer:

#d^2/dx^2 (x^3logx) = x(6logx + 5)#

Explanation:

Using the product rule for the second order derivative:

#d^2/dx^2 (x^3logx) = (d^2/dx^2 x^3)logx +2 (d/dx x^3)(d/dx logx) + x^3(d^2/dx^2 logx)#

#d^2/dx^2 (x^3logx) = 6xlogx +2 xx 3x^2 xx 1/x + x^3(-1/x^2)#

#d^2/dx^2 (x^3logx) = 6xlogx +6x -x#

#d^2/dx^2 (x^3logx) = 6xlogx + 5x#

#d^2/dx^2 (x^3logx) = x(6logx + 5)#