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Mathematics 18 Online
OpenStudy (anonymous):

x^(2x) F'=

myininaya (myininaya):

so it unclear to me what F is?

myininaya (myininaya):

is it that junk before F'=?

OpenStudy (amistre64):

i think its derivative of x^(2x)

myininaya (myininaya):

\[F=x^{2x}\] Take natural log of both sides \[\ln(F)=\ln[x^{2x}]\] \[\ln(F)=2x \ln(x)\] Now differentiate both sides

OpenStudy (amistre64):

thats cool, never did quite learn those

myininaya (myininaya):

\[\frac{F'}{F}=2[ 1 \cdot \ln(x)+x \cdot \frac{1}{x}]\]

myininaya (myininaya):

to solve for F' just multiply F on both sides

myininaya (myininaya):

replace F with x^(2x)

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