Find the equation of the tangent line to the following curve at point (0,pi)
sin(x+y)=2x

I know that to find the equation you will have to take the derivative which will give you the slope which you can then use along with the points to find the equation.
I think that the derivative of the equation is cos(x+y)=2 so cos(x+y)-2=0 would you have to use the chain rule in the center?

Question

Find the equation of the tangent line to the following curve at point (0,pi) 
sin(x+y)=2x 

I know that to find the equation you will have to take the derivative which will give you the slope which you can then use along with the points to find the equation. 
I think that the derivative of the equation is cos(x+y)=2 so cos(x+y)-2=0 would you have to use the chain rule in the center?

anonymous · Answer

d/dx [sin(x+y)] = d/dx [ 2x]

(1+dy/dx) * cos(x+y) = 2
helps ?

anonymous · Answer

you didnt differentiate it correctly

anonymous · Answer

So wait, is it now (2/cos(x+y))-1=dy/dx and then that is the slope?

anonymous · Answer

yes.. it means
y'(x) = (2/cos(x+y))-1
so plug in here the x value of the point and youll have the slope

anonymous · Answer

do you understand how i took the derivative ?

anonymous · Answer

Okay so then m is 2/((cospi)-1) right?

anonymous · Answer

no
m is  (2/cos(pi))-1

anonymous · Answer

so then would the equation be 2/cospi-1x +pi?

anonymous · Answer

first simplify (2/cos(pi))-1 you should know what is this number

anonymous · Answer

OKay so that would be -1?

anonymous · Answer

what is cos(pi) ?

anonymous · Answer

-1

anonymous · Answer

so again what is  (2/cos(pi))-1 ?

anonymous · Answer

$$\frac{ 2 }{ \cos(\pi) } - 1$$

anonymous · Answer

so then it would be -2-1 so -3?

anonymous · Answer

yes -3

anonymous · Answer

sorry for not answering

anonymous · Answer

That is alright Thank you for your help!

anonymous · Answer

yw:)