f(x)=a^x

f'(x)=lim x-->0 /h

(a^x)'=a^x(a^h-1)/h

so ln(x) = lim h-->0 /h or lim h-->00 h

so

ln(x)=

result in st(0)

bye

eko

f'(x)=lim x-->0 /h

(a^x)'=a^x(a^h-1)/h

so ln(x) = lim h-->0 /h or lim h-->00 h

so

ln(x)=

```
```

.data

smallllnumber REAL8 0.00000000001 ; how much accurate

x REAL8 12.0 ; your number

.code

fld smallllnumber

fld x

fyl2x ;x*log2Y

f2xm1 ;Y^x-1

fdiv smallllnumber

result in st(0)

bye

eko

Nice, but isn't this simpler ?

```
fld1
```

fld x

fyl2x

fldl2e

fdiv

if f(a) = a^x

f'(a^x)=x(a^(x-1))

f'(a^x)=x(a^(x-1))

if f(a) = a^x

f'(a^x)=x(a^(x-1))

i meant

(a^x)'

you can consider it as f'(x)

Do you mean that argument of function is x here, and x is logarithm of f(x)=a^x based a?

in other words

if f(x)=a^x

then x = log_a a^x

where a is some constant. ?

so that for example

if a = e

then x =log_e e^x = ln e^x ?

then if delta x here --> 0

then delta function --> 1 since x^0 = 1 if x <> 0

so if f(x)=const^x then 'f(x) =1 with lim_x --> 0

Anyway eko you need transform your

expression: lim h-->00 h

'cause the above means ~ 0.

if h --> 0 then h --> 0. 'Cause x*0=0

You need exclude h in transformations, otherwise the above is useless.

IMHO.

Might be I'm just dummy and you can give some more explanations.

in other words

if f(x)=a^x

then x = log_a a^x

where a is some constant. ?

so that for example

if a = e

then x =log_e e^x = ln e^x ?

then if delta x here --> 0

then delta function --> 1 since x^0 = 1 if x <> 0

so if f(x)=const^x then 'f(x) =1 with lim_x --> 0

Anyway eko you need transform your

expression: lim h-->00 h

'cause the above means ~ 0.

if h --> 0 then h --> 0. 'Cause x*0=0

You need exclude h in transformations, otherwise the above is useless.

IMHO.

Might be I'm just dummy and you can give some more explanations.

f(x)=a^x ; yes a is a constant.

f'(x) = a^x*ln(a)

if a = e its the most beatifaul function . this is the only function that the derivative , integral and the funtion are equal

now we forget about the x

and pay attention only to a

so ln(a)=lim h-->0 /h

that can be write as

lim h-->00 h ;00 as infinite

f'(x) = a^x*ln(a)

if a = e its the most beatifaul function . this is the only function that the derivative , integral and the funtion are equal

now we forget about the x

and pay attention only to a

so ln(a)=lim h-->0 /h

that can be write as

lim h-->00 h ;00 as infinite