18-19 Use implicit differentiation to find dy/dx.18) у сos:4x + 4y4 - y sinA)4yB) -sin|- 4yCos+ y cosy4y2D)-- 4y2sinsin+ у сos- 419) X+Y - x2 + y2x - yA) X(x – y)2 - yx + y(x - y)2B) X(x - y)2 + yx - y(x - y)2C x(x - y)2 + yx + y(x - y)2D) X(x - y)2 - yx - y(x - y)2

18.we have y cos(1y) =4x+4y⇒dydx(cos(1y) )+ysin(1y)×1y2dydx…

Answered: Use implicit differentiation to find…

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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Related questions

Question

18-19

Use implicit differentiation to find dy/dx.
18) у сos
:4x + 4y
4 - y sin
A)
4y
B) -
sin
|- 4y
Cos
+ y cos
y
4y2
D)-
- 4y2
sin
sin
+ у сos
- 4
19) X+Y - x2 + y2
x - y
A) X(x – y)2 - y
x + y(x - y)2
B) X(x - y)2 + y
x - y(x - y)2
C x(x - y)2 + y
x + y(x - y)2
D) X(x - y)2 - y
x - y(x - y)2

Expert Solution

Step 1

$18 . w e h a v e y \cos (\frac{1}{y}) = 4 x + 4 y \Rightarrow \frac{d y}{d x} (\cos (\frac{1}{y})) + y \sin (\frac{1}{y}) \times \frac{1}{y^{2}} \frac{d y}{d x} = 4 + 4 \frac{d y}{d x} \Rightarrow \frac{d y}{d x} (\cos (\frac{1}{y}) + \frac{1}{y} \sin (\frac{1}{y}) - 4) = 4 \Rightarrow \frac{d y}{d x} = \frac{4}{\cos (\frac{1}{y}) + \frac{1}{y} \sin (\frac{1}{y}) - 4} \Rightarrow \frac{d y}{d x} = \frac{4 y}{y c o s (\frac{1}{y}) + s i n (\frac{1}{y}) - 4 y} h e n c e o p t i o n n B i s c o r r e c t$