Question

if y = log `((e^x)/(x^2)) then dy/dx` = ______.

Options

• `(2 − x)/x`

• `(x − 2)/x`

• `(e − x)/e^x`

• `(x − e)/(ex)`

Answer 1

if y = log `((e^x)/(x^2)) then dy/dx` = `bbunderline((x − 2)/x)`.

Explanation:

y = log `(e^x/x^2)`

Use log properties:

y = `log(e^x) − log(x^2)`

y = x − 2log x

Differentiate:

`dy/dx = (1 − 2)/x`

`dy/dx = (x − 2)/x`