Question

1. a) Use the Chain Rule to calculate the partial derivatives. Express the answer in terms...

1.

a) Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables.

∂f
∂r
∂f
∂t

;    f(x, y, z) = xy + z2,    x = r + s − 2t,    y = 6rt,    z = s2

∂f
∂r
=
∂f
∂t
=

b) Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent variables.

∂F
∂y

;    F(u, v) = eu+v,    u = x5,    v = 2xy

∂F
∂y

=

c)

Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the independent variables.

∂f
∂u

;    f(x, y) = x2 + y2,    x = eu+v,    y = 2u + 4v

∂f
∂u

=

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f(x,y,z)=xy+z^3, x=r+s−8t, y=3rt, z=s^6. Use the Chain Rule to calculate the partial derivatives. (Use symbolic...
Let f(x,y,z)=xy+z^3, x=r+s−8t, y=3rt, z=s^6. Use the Chain Rule to calculate the partial derivatives. (Use symbolic notation and fractions where needed. Express the answer in terms of independent variables
Let f(x,y,z)=6xy−z^2, x=6rcos(θ), y=cos^2(θ), z=7r. Use the Chain Rule to calculate the partial derivative. (Use symbolic...
Let f(x,y,z)=6xy−z^2, x=6rcos(θ), y=cos^2(θ), z=7r. Use the Chain Rule to calculate the partial derivative. (Use symbolic notation and fractions where needed. Express the answer in terms of independent variables
Use the Chain Rule to evaluate the partial derivative ∂f∂u and ∂f∂u at (u, v)=(−1, −1),...
Use the Chain Rule to evaluate the partial derivative ∂f∂u and ∂f∂u at (u, v)=(−1, −1), where f(x, y, z)=x10+yz16, x=u2+v, y=u+v2, z=uv. (Give your answer as a whole or exact number.) ∂f∂u= ∂f∂v=
Use the Chain Rule to find the indicated partial derivatives. R = ln(u2 + v2 +...
Use the Chain Rule to find the indicated partial derivatives. R = ln(u2 + v2 + w2), u = x + 3y,    v = 5x − y,    w = 2xy; when x = y = 2 dR/dx= dR/dy=  
Use the Chain Rule to find the indicated partial derivatives. u = r2 + s2 ,    r...
Use the Chain Rule to find the indicated partial derivatives. u = r2 + s2 ,    r = y + x cos t,    s = x + y sin t ∂u ∂x ,   ∂u ∂y ,   ∂u ∂t     when x = 2,  y = 5,  t = 0
Use the Chain Rule to find the indicated partial derivatives. u = x^4 + yz, x...
Use the Chain Rule to find the indicated partial derivatives. u = x^4 + yz, x = pr sin(θ), y = pr cos(θ), z = p + r; (partial u)/(partial p), (partial u)/(partial r), (partial u)/(partial theta) when p = 3, r = 4, θ = 0
Use the Chain Rule to find the indicated partial derivatives. z = x2 + xy3, x...
Use the Chain Rule to find the indicated partial derivatives. z = x2 + xy3, x = uv2 + w3, y = u + vew when u = 2, v = 2, w = 0
Use the Chain Rule to find the indicated partial derivatives. u =sqrt( r^2 + s^2) ,...
Use the Chain Rule to find the indicated partial derivatives. u =sqrt( r^2 + s^2) , r = y + x cos(t), s = x + y sin(t) ∂u ∂x , ∂u ∂y , ∂u ∂t when x = 1, y = 4, t = 0
Use the Chain Rule to find the indicated partial derivatives. P = sqrt(u2 + v2 +...
Use the Chain Rule to find the indicated partial derivatives. P = sqrt(u2 + v2 + w2),    u = xey,    v = yex,    w = exy; when x=0 and y=2. ∂P ∂y and ∂P ∂x
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of...
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t.) z = tan(u/v), u = 3s + 7t, v = 7s - 3t