Question

find the eqaution of the tangent plane at the point (2,2) on the surface z = sin (x^y)

Answer 1

1)first find the derivative of the following equation = m =equation of the slope
2) substitute x to find the slope
3) substitute the rest of your given in the following equation to find the equation of the tangent line :
yp - y = m(x - xp)

and simply solve

^_^ clearer now?

Answer 2

the question is not asking about the tangent line in 2D, but about the tangent plane on a surface

Answer 3

is it
\[z=\sin (xy)\]

Answer 4

lol sorry ^^"

Answer 5

Would this involve the del operator (sum of partial derivatives)?

Answer 6

let \[f(x,y,z)=z-\sin(xy)\]
grad f(x,y,z) = \[<-ycos(xy),-xcos(xy),1>\]
grad f(2,2,z)= <-2cos(4),-2cos(4),1>

Answer 7

the equation of the tangent plane will be:
-2cos(4)(x-2)-2cos(4)(y-2)+(z-sin(4))=0
simplify!!

Answer 8

I gotta go now