Answered: 5. Differentiate a) y²=3x²y+4xy² b)… | bartleby

Calculus: Early Transcendentals

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

5. Differentiate
a) y²=3x²y+4 xy²
2x²-3x+1
b) _y=² 2x+2

Expert Solution

Step 1

Given :

a) $y^{2} = 3 x^{2} y + 4 x y^{2}$

b) $y = (\frac{2 x^{2} - 3 x + 1}{2 x + 2})$

To differentiate the given function.

Following differentiating formulas are used-

$\begin{array}{rcl} \frac{d}{d x} (f (x) \pm g (x)) & = & \frac{d}{d x} (f (x)) \pm \frac{d}{d x} (g (x)) \\ \frac{d}{d x} (a f (x)) & = & a \frac{d}{d x} (f (x)) \\ \frac{d}{d x} (f (x) g (x)) & = & f (x) \frac{d}{d x} (g (x)) + g (x) \frac{d}{d x} (f (x)) \\ \frac{d}{d x} (x^{n}) & = & n x^{n - 1} \\ \frac{d}{d x} (a x) & = & a \\ \frac{d}{d x} (a) & = & 0 \end{array}$

Here, $a$ is the constant and $f (x)$ and $g (x)$ are the differentiable functions.

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