Was ist die Ableitung von # 3 ^ x #?

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)|)))#