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Mathematics 20 Online
OpenStudy (anonymous):

how do I differentiate the series ab^(a-1) and series ab^a.

OpenStudy (anonymous):

\[\sum_{a=1}^{\infty}\]

OpenStudy (misty1212):

HI!!

OpenStudy (misty1212):

can you be a bit more specific?

OpenStudy (anonymous):

hello :)

OpenStudy (misty1212):

\[\sum_{n=1}^{\infty}\] really doesn't mean anything by itself

OpenStudy (anonymous):

\[\sum_{a=1}^{\infty} a b^{a-1}\]

OpenStudy (misty1212):

differentiate term by term

OpenStudy (misty1212):

what you wrote is the derivative of \[\sum_{a=1}^{\infty}b^a\]

OpenStudy (anonymous):

so your saying differentiate ab^a would be a^2 * b^(a+1)

OpenStudy (misty1212):

no

OpenStudy (misty1212):

the derivative of \(b^a\) wrt \(b\) is \( ab^{a-1}\)

OpenStudy (misty1212):

the derivative of \(ab^{a-1}\) wrt \(b\) is \(a(a-1)b^{a-2}\)

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