A trick for you guys,maybe you know it but i just want to share it.

Question

hba · Answer

Let me show you a trick 


differentiate 

$$e ^{x}sinx$$

the differential would be

$$e^x(sinx+cosx)$$


You just take the e^x out of the bracket and then write sinx and then diffrentiate it and write what comes.

Let me show you another example


differentiate



$$e^x tanx$$

the differential would be 

$$e^x(tanx+\sec^2x) $$

In this case you also leave the e^x and then write tanx in the bracket and then diffrentiate it and you get sec^2x


Let us form a general formula out of it.

$$e^x x$$

so to diffrentiate it

$$e^x(x+\frac{ d(x) }{ dx })$$

hartnn · Answer

$[e^xf(x)]'=e^x(f(x)+f'(x))$
works only for e^x, not for $e^{ax}$.

hba · Answer

Yeah.

hartnn · Answer

$[e^{ax}f(x)]'=e^x(af(x)+f'(x))$

anonymous · Answer

to much smart ppl, must go dumb down..

unklerhaukus · Answer

nice

dls · Answer

that is the original way how i do it lol :D

hba · Answer

Well i was taught this as a trick lol :D