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

1 Answer
May 15, 2017

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

Explanation:

#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)#