What is the equation of the line tangent to $f(x)=e^xsinx/x$ at $x=pi/3$ ?

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Answer 1 · 2017-05-15T14:48:22

$(y-2.35564)=1.46682(x-pi/3)$

$d/dx[(e^xsin(x))/x]=((d/dx[e^xsin(x)])(x)-(1)(e^xsin(x)))/x^2=(e^x(sin(x)+cos(x))(x)-e^xsin(x))/x^2=(e^x xsin(x)+e^x xcos(x)-e^xsin(x))/x^2->$

Substitute $pi/3$ in the derivative, $m=1.46682$

Substitute $pi/3$ in the original function

$f(pi/3)=(e^(pi/3)sin(pi/3))/(pi/3)=2.35564$

Putting it all together:
$(y-2.35564)=1.46682(x-pi/3)$

What is the equation of the line tangent to f(x)=e^xsinx/x f(x)=e^xsinx/x at x=pi/3 x=pi/3?