Januar 30, 2020

von Ruperta

Was ist die Ableitung von $3 ^ x$ ?

Antworten:

$3^xln3$

Erläuterung:

Begin by letting $y=3^x$

now take the ln of both sides.

$lny=ln3^xrArrlny=xln3$

differentiate $color(blue)"implicitly with respect to x"$

$rArr1/y dy/dx=ln3$

$rArrdy/dx=yln3$

now y = $3^xrArrdy/dx=3^xln3$

This result can be $color(blue)"generalised"$ as follows.

$color(red)(bar(ul(|color(white)(a/a)color(black)(d/dx(a^x)=a^xlna)color(white)(a/a)|)))$