Question

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

Answer 1

`(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)`