f(x) = c abx + d
= c abxad
integrating and differentiating exponential functions
Author
how can i integrate and differentiate functions in the form
For differentiation it should be something like this...
f(x) = c * a^bx * a^d
= c*(a^d) * a^bx
ln(f(x)) = ln(c*(a^d)* a^bx)
= ln(c*(a^d)) + ln(a^bx)
= ln(c*(a^d)) + (ln(a)*b) * x
f(x) = e^(ln(c*(a^d)) + (ln(a)*b) * x)
f'(x) = ln(a)*b* e^(ln(c*(a^d)) + (ln(a)*b) * x)
I think thats right, please correct me if i'm wrong...
-- Steven Ashley
f(x) = c * a^bx * a^d
= c*(a^d) * a^bx
ln(f(x)) = ln(c*(a^d)* a^bx)
= ln(c*(a^d)) + ln(a^bx)
= ln(c*(a^d)) + (ln(a)*b) * x
f(x) = e^(ln(c*(a^d)) + (ln(a)*b) * x)
f'(x) = ln(a)*b* e^(ln(c*(a^d)) + (ln(a)*b) * x)
I think thats right, please correct me if i'm wrong...
-- Steven Ashley
I found this page that might be useful for you. It lists all basic differentiation and integration formulas.
http://library.thinkquest.org/20991/calc/reference.html
Hope it helps a little ;o)
Y.
Now i see AP is right on that derivation it is c.[b*len(a)*a^(bx+d) ]
but as for the integral, i'm not sure, cos' i'm long from the school ;o)
http://library.thinkquest.org/20991/calc/reference.html
Hope it helps a little ;o)
Y.
Now i see AP is right on that derivation it is c.[b*len(a)*a^(bx+d) ]
but as for the integral, i'm not sure, cos' i'm long from the school ;o)
home-work?
easy.
Note that ax=ex*ln(a)
let k=c*ad and l=ln(a)*b
so we have
f(x)=k*el*x
Now, using most basic methods of integration you REALLY need to remember,
F(x)=integral f(x)=(k/l)*el*x + const
and
f'(x)=k*l*el*x
Quote:Original post by Genjix
how can i integrate and differentiate functions in the formf(x) = c abx + d = c abxad
thanks.
easy.
Note that ax=ex*ln(a)
let k=c*ad and l=ln(a)*b
so we have
f(x)=k*el*x
Now, using most basic methods of integration you REALLY need to remember,
F(x)=integral f(x)=(k/l)*el*x + const
and
f'(x)=k*l*el*x
Author
Quote:Original post by Dmytry
home-work?
no, this was just me trying to find a general way to differentiate and integrate exponentials which I have been using quite a lot
(genetic curve fitting :))
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