
Partial derivatives and chain rule
230869 Partial derivatives and chain rule Find (partial z)/(partial u)( and ) (partial z)/(partial v) using the chain rule. Assume the variables are restricted to domains on which the functions are defined.

Partial derivatives
Find the indicated partial derivatives.
1.) f(x,y)= sin(yx); df/dx(3,3)
Using the chain rule,
Therefore, at (x, y) =(3, 3),
2.)z= (x^3 + y^3)/(x^2 + y^2); dz/dx, dz/dy
Using chain rule and quotient rule,
Similar to x, we find the

Partial Derivatives using Chain Rule
Two multivariable formulas are given and partial derivatives of both are found using the chain rule.

Apply the chain rule to finding partial derivatives.
The chain rule to is applied to finding partial derivatives.

Partial Derivatives and Appropriate Chain Rule
9015 Partial Derivatives and Appropriate Chain Rule Find partial deriv's w/r and w/theta using appropriate chain rule for :
w=the square root of (255x^25y^2), where x=r cos theta, y= r sin theta. w = (25  5r^2(cos^2 (theta) + sin^2(theta)))^1/2 or

Chain Rule : Finding Where f is Differentiable
Using the chain rule, show that if z = y + f(x^2  y2), where f is differentialbe,
then partial derivatives y(dz/dx) + x(dz/dy) = x
Solution:
The chain rule for a function of two variables is given by,
If z=f(x, y) is differentiable and x

Chain rule
z); x=x(u, v), y=y(u, v), z=z(u, v)
Thus we have the following partial derivatives:
dp/du=(df/dx)(dx/du)+(df/dy)(dy/du)+(df/dz)(dz/du)
dp/dv=(df/dx)(dx/dv)+(df/dy)(dy/dv)+(df/dz)(dz/dv) This shows how to write chain rule formulas giving the partial

Function, derivatives, error, and stationary points.
Determine the secondorder Taylor polynomial for f near (0,1)
Use firstorder partial derivatives to determine the least and greatest possible values.
Use the chain rule to determine, in terms of t, the rate of change of f.

Using the Chain rule for derivatives in higher dimension
204667 Using the Chain rule for derivatives in higher dimension Let f(u,v,w) = (euw, cos(v+u)+sin(u+v+w)) and g(x,y) = (ex, cos(yx), ey). Calculate f o g and D(f o g)(0,0). The solution is attached.