Given f(x)= \[e^{ax}\]
let first derivative be \[y_1\]= \[ae^{ax}\]
\[y_2\]= \[(a^2)e^{ax}\]
\[y_3\]= \[(a^3)e^{ax}\]
\[y_4\]= \[(a^4)e^{ax}\]
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similarly \[y_n\]= \[(a^n)e^{ax}\]
problem
Find the 2nd derivative of the function f(x)= \[e^{2x}\] at x=0.5
solution
for a=2 n=2 and x=0.5 we get \[y_2\]=10.87312
Now for f(x)= \[e^{ax+b}\]
\[y_1\]= \[ae^{ax+b}\]
\[y_2\]= \[(a^2)e^{ax+b}\]
\[y_3\]= \[(a^3)e^{ax+b}\]
\[y_4\]= \[(a^4)e^{ax+b}\]
...................................
.....................................
similarly \[y_n\]= \[(a^n)e^{ax+b}\]
problem
Find the 2nd derivative of the function f(x)= \[e^{2x+1}\] at x=0.5
solution
for a=2 n=2 and x=0.5
here b=1
on putting these values in above formula we get \[y_2\]=29.5561
