Question

Question #7454e

Answer 1

`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)`