A level - Find the coordinates of the stationary point of the curve with equation : (x+y-2)^2 + e^y -1

Immediately by reading the question we know that differentiation will need to bee used as we are asked to find the stationary point and this is found by equating the derivative equal to 0.Knowing this, firstly I expanded the left hand side out to make the differentiation easier. We can see that there are both functions of x and functions of y meaning that implicit differentiation is going to be needed, this is when you differentiation both x and y with respect to x. You differentiate the x functions as normal as it is with respect to x, by multiplying by the original power and then subtracting one from the power. For functions of y you differentiate normally as if it was with respect to y but you then also multiply by dy/dx to make sure everything is still in respect to x. For the functions which have both x and y in, you use the product rule and follow the same rules with x and y functions. Next, I move all the components with dy/dx onto the left hadn't side and all the components without to the right hand side.I then factorise the left by dy/dx and divide the right hand side by the factorisation of dy/dx.We have now got the derivative of the equations and can find the stationary point, using out knowledge of the stationary point being at dy/dx=0, we set our derivative to 0 and rearrange for and equation with x in terms of y.We then sub this into the original equation which finds us the y co-ordinate and then sub our y into our equation of x in terms of y to find our x co-ordinate. This then gives the answer of - (2,0)