Use the Chain Rule to calculate the partial derivatives
?(?,?)=cos(?2+?2) ?=2?+3?, ?=3?+3?
∂?∂?=
∂?∂?=
Use the Chain Rule to calculate the partial derivatives
?(?,?)=cos(?2+?2) ?=2?+3?, ?=3?+3?
∂?∂?=
∂?∂?=
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the...
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...
Use the Chain Rule to find the indicated partial derivatives. ?
= ?^ 2 + ?^...
Use the Chain Rule to find the indicated partial derivatives. ?
= ?^ 2 + ?^ 2 , ? = ?? cos ? , ? = ?? sin ?
??/??, ??/?? , ??/?? ?ℎ?? ? = 2, ? = 3, ? = 0°
Consider the function F(x, y, z) =x2/2−
y3/3 + z6/6 − 1.
(a) Find the gradient...
Consider the function F(x, y, z) =x2/2−
y3/3 + z6/6 − 1.
(a) Find the gradient vector ∇F.
(b) Find a scalar equation and a vector parametric form for the
tangent plane to the surface F(x, y, z) = 0 at the point (1, −1,
1).
(c) Let x = s + t, y = st and z = et^2 . Use the multivariable
chain rule to find ∂F/∂s . Write your answer in terms of s and
t.
Consider the surface S in R3 defined implicitly by x**2 y =
4ze**(x+y) − 35 ....
Consider the surface S in R3 defined implicitly by x**2 y =
4ze**(x+y) − 35 .
(a) Find the equations of the implicit partial derivatives ∂z ∂x
and ∂z ∂y in terms of x, y, z. (b) Find equations of the tangent
plane and the norma line to the surface S at the point (3, −3,
2)