The task is to find the partial derivatives $\partial w/\partial s$ and $\partial w/\partial t$ using the Chain Rule.**Function:**\[ w = y^3 - 2x^2y^5 \]**Values:**\[ s = -3, \quad t = 6 \]\[ x = e^s, \quad y = e^t \]**Partial Derivatives to Find:**1. $\partial w/\partial s$ - Calculation: \[ \partial w/\partial s = -4 \] - The given answer (-4) is marked incorrect (indicated by a red "X").2. $\partial w/\partial t$ - Calculation: \[ \partial w/\partial t = 3e^{18} - 2 \] - This result is also marked incorrect (indicated by a red "X").**Evaluation at Given Values:**- Evaluate each partial derivative at $s = -3$ and $t = 6$.1. $\partial w/\partial s$ - Calculation: \[ \partial w/\partial s = 3e^{18} - 2 \] - This result is marked incorrect (indicated by a red "X").2. $\partial w/\partial t$ - Calculation: \[ \partial w/\partial t = -3 \] - This result is marked incorrect (indicated by a red "X").

To find by using the appropriate Chain Rule.Function: Values: To evaluate each partial derivate at…

Answered: Find aw/as and aw/at using the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The task is to find the partial derivatives $\partial w/\partial s$ and $\partial w/\partial t$ using the Chain Rule.

**Function:**
\[ w = y^3 - 2x^2y^5 \]

**Values:**
\[ s = -3, \quad t = 6 \]
\[ x = e^s, \quad y = e^t \]

**Partial Derivatives to Find:**

1. $\partial w/\partial s$

- Calculation:
\[
\partial w/\partial s = -4
\]
- The given answer (-4) is marked incorrect (indicated by a red "X").

2. $\partial w/\partial t$

- Calculation:
\[
\partial w/\partial t = 3e^{18} - 2
\]
- This result is also marked incorrect (indicated by a red "X").

**Evaluation at Given Values:**

- Evaluate each partial derivative at $s = -3$ and $t = 6$.

1. $\partial w/\partial s$

- Calculation:
\[
\partial w/\partial s = 3e^{18} - 2
\]
- This result is marked incorrect (indicated by a red "X").

2. $\partial w/\partial t$

- Calculation:
\[
\partial w/\partial t = -3
\]
- This result is marked incorrect (indicated by a red "X").

Expert Solution

Step 1: Define the problem.

To find $fraction numerator partial differential straight w over denominator partial differential straight s end fraction space and space fraction numerator partial differential straight w over denominator partial differential straight t end fraction$ by using the appropriate Chain Rule.

Function:

$straight w equals straight y cubed minus 2 straight x squared straight y straight x equals straight e to the power of straight s straight y equals straight e to the power of straight t$

Values:

$straight s equals negative 3 comma space straight t equals 6$

To evaluate each partial derivate at the given values.