Posted by Fred on Saturday, April 17, 2010 at 10:28am.
If f(x) = (e^(x))sin(x) what is the 1000th derivative?
Step are needed and the general rule/pattern
Calculus - Reiny, Saturday, April 17, 2010 at 10:43am
y = e^x(sinx)
yI = e^xcosx + e^xsinx
= e^x(cosx + sinx)
yII = e^x(-sinx + cosx) + e^x(cosx + sinx)
= e^x(2cosx) = 2e^x(cosx)
yIII = 2e^x(-sinx) + 2e^x(cosx)
= 2e^x(cosx - sinx)
yIV = 2e^x(-sinx-cosx) + 2e^x(cosx - sinx)
Ahhh so it took 4 derivatives to reach -4(what we started with)
so yVIII would be (-4)(-4)e^x(sinx)
so y1000= (-4)^250(e^x(sinx))
Calculus - Joey, Saturday, April 17, 2010 at 10:47am
where did u get the 250 from?
Calculus - Damon, Saturday, April 17, 2010 at 10:51am
every fourth one is 4 times four before it.
1000/4 is 250
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