find an equation of the tangent line to the curve at the given point y=sin x +cos x (0,1)

Question

Please help me 

Answer 1

The slope of the tangent line is the derivative.  We need to find the derivative of the function.

 

y' = cos(x) - sin(x)

 

 

Plug in x=0 to find evaluate y'.

 

y' = cos(0) - sin(0)

y' = 1

 

 

So far, the equation of the tangent line is     y = x + b

 

Plug in the value of the coordinate into the equation to find b.

 

1 = 0 + b

1 = b

 

 

The equation of the tangent line is

 

y = x + 1