Question

What is the derivative of `f(x) = 1/xlnx`?

Answer 1

`(1-ln(x))/x^2`

Explanation:

Use the product rule: you have that

`d/dx f(x)*g(x) = f'(x)*g(x) + f(x)*g'(x)`.

Let's write down the quantity we need:

• `f(x)= 1/x`;
• `g(x)=ln(x)`;
• `f'(x)=-1/x^2`;
• `g'(x) = 1/x`.

Plugging these functions into the product rule, you have

`-1/x^2 * ln(x) + 1/x * 1/x = -ln(x)/x^2+1/x^2 = (1-ln(x))/x^2`