Question

What is the second derivative of y=log (x^2/e^x)?

Answer 1

$y = log( \frac{ {x}^{2} }{ {e}^{x} } ) \\ \frac{dy}{dx} = \frac{1}{ \frac{ {x}^{2} }{ {e}^{x} } } \times \frac{2x {e}^{x} - {x}^{2} {e}^{x} }{ {e}^{2x} } \\ \frac{dy}{dx} = \frac{2x - {x}^{2} }{ {x}^{2} } \\ \frac{ {d}^{2}y }{d {x}^{2} } = \frac{(2 - 2x) {x}^{2} - (2x - {x}^{2} ) \times 2x}{ {x}^{4} }$
hope this will help you.