Question

Find the second order derivatives of the following function x³ log x ?

Answer 1

We have,

\[y = x^3 \log x\]

\[\text { Differentiating w . r . t . x, we get }\]

\[\frac{d y}{d x} = 3 x^2 \log x + x^3 \times \frac{1}{x}\]

\[ = 3 x^2 \log x + x^2 \]

\[\text { Differentiating again w . r . t . x, we get }\]

\[\frac{d^2 y}{d x^2} = 6x \log x + 3 x^2 \times \frac{1}{x} + 2x\]

\[ = 6x \log x + 5x\]