Mathematics
OpenStudy (anonymous):

find an equation of the tangent line to the graph of y=xlnx at the point (1,0)

myininaya (myininaya):

$y'=(1) \ln(x)+x \frac{1}{x}=\ln(x)+1$

myininaya (myininaya):

$y'|_{x=1}=\ln(1)+1=0+1=1$

myininaya (myininaya):

$y=x+b$

myininaya (myininaya):

we need to find b the y-intercept

myininaya (myininaya):

we know a point on this line: (1,0)

myininaya (myininaya):

0=1+b=> -1=b=> b=-1

myininaya (myininaya):

$y=x-1$