Answer Happy

State the Chain Rule:
z = f (x, y) is a differentiable function and x = s(t), y = p(t) - are functions of one variable, then:
dz/dt=
z = f (x,y) is a differentiable function, where x = q(s, t), y = p(s, t) - are functions of two variables, then:
∂z/∂s=
∂z/∂t=
Find the local maximum, minimum values and saddle point(s) of the function, if any.
f(x,y)=xy-2x-2y-x^2-y^2
Find the first partial derivatives for s(u, t) = (u+2t)/(u^2+t^2 ) evaluated at s(2, 1).
For the function z = ex cos(y) find the equation of
The tangent plane to the given surface at point (0, 0, 1).
The normal line to the given surface at point (0, 0, 1).
1. State the Chain Rule: a. z = f (x, y) is a differentiable function and x = s(t), y = p(t) - are functions of one variable, then: dz dt = b. z = f(x) is a differentiable function, where x = g(s, t), y = p(s, t) - are functions of two variables, then: дz əs дz at || 2. Find the local maximum, minimum values and saddle point(s) of the function, if any. f(x,y) = xy - 2x - 2y - x² - y² 3. Find the first partial derivatives for s(u, t) = - u+2t u²+t² evaluated at s(2, 1). 4. For the function z = ex cos(y) find the equation of a. The tangent plane to the given surface at point (0, 0, 1). b. The normal line to the given surface at point (0, 0, 1).