What is the derivative of $\frac{ln x}{e^{x}}$ $ln x / e^x$ ?

Question

1448 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-25T19:22:43

First, we can rewrite this expression as a product instead of a quotient:

$ln (x) e^{- x}$ $ln(x)e^-x$

And, now, remembering the product rule:

Be $y = f (x) g (x)$ $y=f(x)g(x)$ , then $(dy)/(dx)=f'(x)g(x)+f(x)g'(x)$ , we'll get

$(dy)/(dx)=1/x*e^-x+ln(x)(-e^-x)$

$(dy)/(dx)=color(green)(e^-x(x^-1+ln(x)))$

What is the derivative of ln x / e^xlnxexln x / e^x?