Question

How do you find the equation of the tangent line to the curve `y=e^x sin x`at point (0,0)?

Answer 1

I found: `y=x`

Explanation:

First find the slope `m` of the tangent evaluating the derivative at the point of interest:
`y'=e^xsin(x)+e^xcos(x)` (Product Rule);
evaluate this derivative at `x=0`:
`y'(0)=0+1=1=m`
Use the relationship:
`y-y_0=m(x-x_0)`
to find the equation of the tangent:
`y-0=1(x-0)`
`y=x`

Graphically: