### Calculus: Partial Derivatives#### Problem 50a) **Assume that $ w = f(s^3 + t^2) $ and $ f'(x) = e^x $. Find** \[ \frac{\partial w}{\partial t} \quad \text{and} \quad \frac{\partial w}{\partial s}. \]To solve this problem, you'll need to apply the chain rule for partial derivatives.b) **Assume that $ w = f(ts^2, \frac{s}{t}) $, $ \frac{\partial f}{\partial x}(x, y) = xy $, and $ \frac{\partial f}{\partial y}(x, y) = \frac{x^2}{2} $. Find** \[ \frac{\partial w}{\partial t} \quad \text{and} \quad \frac{\partial w}{\partial s}. \]This part requires using the partial derivatives and applying them to a function with multiple variables.In both parts, understanding how to use the chain rule and partial differentiation is crucial in breaking down the functions and finding the required derivatives. Each step involves differentiating with respect to one variable while treating the other variables as constants and then applying the given derivative information.

a) and To find: and b) , , and To find: and

Answered: ow 50. a) Assume that w = f(s³ + t²)…

Calculus: Early Transcendentals

8th Edition

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Author:James Stewart

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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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ow 50. a) Assume that w = f(s³ + t²) and f'(x) = e*. Find and dw at მs` af af b) Assume that w = f(ts², ;), of (x, y) = xy, and ду (x, y) = . Find and dw at dw as