x^2 + y^2 +z^2 = 1

Let (a,b,c) be a point on the surface, find the equation of plane tangent to this surface at (a, b, c)

Do I put it in terms of z?

f(x,y) = z = sqroot( 1-x^2-y^2)

Solve for fx(x,y) and fy(x,y) and plugging in 'a' and 'b' for x and y

z= (fx(a,b)(x-a) + (fy(a,b)(y-b) + c

Is this correct? Thanks in advance.