34. ey sin x = x + xy

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 36CR
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Use Equation 5 to find dy/dx

5
dy
Transcribed Image Text:5 dy
34. ey sin x = x + xy
Transcribed Image Text:34. ey sin x = x + xy
Expert Solution
Step 1

Given: eysinx=x+xy

Step 2

Explanation:

Let Fx,y=eysinx-x-xy            ........(i)

Then we have

dydx=-FxFy=-FxFy                ......(ii)

Partially differentiating equation (i) with respect to 'x' and 'y' respectively

Fx=eycosx-1-yFy=eysinx-x

Therefore, from (ii) 

dydx=-eycosx-1-yeysinx-x 

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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,