1. Let $ y = f(x) $. Compute the following:(a) $\frac{d}{dx}(xy) =$(b) $\frac{d}{dx}(x^2y) =$(c) $\frac{d}{dx}(xy^2) =$

Name: 1. Let $ y = f(x) $. Compute the following:(a) $\frac{d}{dx}(xy) =
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Description: 1. Let \( y = f(x) $. Compute the following:(a) $\frac{d}{dx}(xy) =$(b) $\frac{d}{dx}(x^2y) =$(c) $\frac{d}{dx}(xy^2) =$

(a) Derivative: ddxxy Differentiate the given expression. ddxxy=xddxy+yddxx=x0+y1=y

Answered: (a) (ry) = (b) (c)

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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1. Let $ y = f(x) $. Compute the following:

(a) $\frac{d}{dx}(xy) =$

(b) $\frac{d}{dx}(x^2y) =$

(c) $\frac{d}{dx}(xy^2) =$

Expert Solution

Step 1

(a)

Derivative: $\frac{d}{d x} (x y)$

Differentiate the given expression.

$\begin{array}{rcl} \frac{d}{d x} (x y) & = & x (\frac{d}{d x} y) + y (\frac{d}{d x} x) \\ = & x (0) + y (1) \\ = & y \end{array}$

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