Understanding derivative of e ax requires examining multiple perspectives and considerations. $n$th derivative of $e^ {ax}\sin (bx+c)$ - Mathematics Stack Exchange. How can we substitute $r \\cos \\alpha$ and $r \\sin \\alpha$ for $a$ and $b$? How, on successive differentiation, is there another $r$ multiplied? calculus - Find the $n^ {th}$ derivative of $y=e^ {ax}.x^3 .... What sort of result are you hoping for?
Another key aspect involves, it's easy, say, to get $y^ { (n)}$ at $x=0$ or something like that. In this context, otherwise, the answer is $ (A_nx^3+B_nx^2+C_nx+D_n)e^ {ax ... How to find the $n$-th derivative of $y=e^{ax+b}$ Please provide an explanation of the steps.
Furthermore, dirac delta function in the second derivative of $e^{-a|x|}$. The delta function comes due to the non-differentiability of the absolute value function at the point $0$. In that case, a delta function (centered at zero) gets added. Furthermore, the coefficient of the delta function is the "jump" of the function at the point i.e. the right limit minus the left limit at the point.
In this case, it is $-2a$, hence we see that the factor $-2a\delta (x)$ gets ... Integrate $e^ {-ax}$ and $xe^ {-ax}$? Equally important, - Mathematics Stack Exchange. A trick for the second one is to consider it a derivative of the first function with respect to a. Is not really formal, but really useful.
It goes like this: $$\int_0^\infty Ax\exp (-ax)=-A\int_0^\infty \frac {d} {da}\exp (-ax)dx=-A\frac {d} {da}\int_0^\infty\exp (-ax)dx$$ The integral of the first one is easy, it's just $-\frac {1} {a}\exp (-ax)$, as said in the posts. Using the Limit definition to find the derivative of $e^x$. Another key aspect involves, calculus - Nth derivative of the function y=$e^ {ax}\sin {bx ....
Nth derivative of the function y=$e^ {ax}\sin {bx}$ Ask Question Asked 6 years, 1 month ago Modified 6 years, 1 month ago Why is the derivative of - Mathematics Stack Exchange. If the derivative is with respect to x x, then x x is in the exponent. Please don't confuse this with the derivative of xn x n.
derivatives - What is the difference between exponential symbol $a^x .... What definition I have for the logarithm without the exponential? Similarly, i guess you could define it as the integral $\int_1^t (1/x)dx$. But people see the exponential before they see integrals I think usually.
The right definition, in my opinion, is as the inverse of the exponential.
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