Use the Chain Rule to find the indicated partial derivatives. u = r^2 + s^2, r = y + x cos(t), s = x + y sin(t) ∂u/∂x, ∂u/∂y, ∂u/∂t when x = 5, y = 2, t = 0
Added by Eva B.
Step 1
Given $u = r^2 + s^2$, $r = y + x\cos(t)$, and $s = x + y\sin(t)$. We have $\frac{\partial u}{\partial x} = \frac{\partial u}{\partial r} \cdot \frac{\partial r}{\partial x} + \frac{\partial u}{\partial s} \cdot \frac{\partial s}{\partial x}$. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Harshita Goel and 63 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use the Chain Rule to find the indicated partial derivatives. u = r^2 + s^2, r = y + x cos(t), s = x + y sin(t) ∂u/∂x, ∂u/∂y, ∂u/∂t when x = 1, y = 5, t = 0
Israel H.
Use the Chain Rule to find the indicated partial derivatives. $$ \begin{array}{l} z=x^{4}+x^{2} y, \quad x=s+2 t-u, \quad y=s t u^{2} \\ \frac{\partial z}{\partial s}, \frac{\partial z}{\partial t}, \frac{\partial z}{\partial u} \quad \text { when } s=4, t=2, u=1 \end{array} $$
Partial Derivatives
The Chain Rule
Use appropriate forms of the chain rule to find the derivatives. $$ \begin{array}{l}{\text { Let } w=r s /\left(r^{2}+s^{2}\right) ; r=u v, s=u-2 v . \text { Find } \partial w / \partial u} \\ {\text { and } \partial w / \partial v}\end{array} $$
PARTIAL DERIVATIVES
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD