Question

find dx/dx and dz/dy

z^3 y^4 - x^2 cos(2y-4z)=4z

Answer #1

Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz where
C is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (Hint:
Observe that C lies on the surface z = 2xy.) C F · dr =

Let w(x,y,z) = x^2+y^2+z^2 where x=sin(8t), y=cos(8t) , z=
e^t
Calculate dw/dt by first finding dx/dt, dy/dt, and dz/dt and using
the chain rule
dx/dt =
dy/dt=
dz/dt=
now using the chain rule calculate
dw/dt 0=

List these six partial derivatives for z = 3 x2 y +
cos (x y) – ex+y
dz/dx dz/dy d2z/dx2 d2z/
dy2 d2z/dxdy d2z/dydx
Evaluate the partial
derivative
dz at the point (2, 3,
30) for the function z = 3 x4 – x y2
dx

Evaluate double integral Z 2 0 Z 1 y/2 cos(x^2 )dx dy
(integral from 0 to 2)(integral from y/2 to 1) for cos(x^2) dx
dy

Find the first derivative of each
Y=3Z1/2+2Z-1/2-5Z-4/5
dY/dZ =
Y=4X3/4+3X-1/3-2X3/2
dY/dX =
R=3S1/2(3-2S+5S^2)
dR/dS=

Find the derivatives dy/dx and d^2y/dx^2, and evaluate them at t
= 2.
x=t^2 ,y = t ln t

Evaluate Integral (subscript c) z dx + y dy − x dz, where the
curve C is given by c(t) = t i + sin t j + cost k for 0 ≤ t ≤
π.

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

Find dy/dx by implicit differentiation:
A.). x^4 + y^3 = 3
B.). 5x^2 +3xy - y^2 =7
C.) x^3(x+y) = y^2(4x-y)

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

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