   Chapter 2.6, Problem 17E

Chapter
Section
Textbook Problem

# Find d y / d x by implicit differentiation. x y = 1 + x 2 y

To determine

To find:

dydx

by Implicit differentiation.

Explanation

1) Formula:

i. Sum and difference rule of differentiation:

ddxfx ±gx=ddx fx± ddxgx

ii. Constant rule:

ddxc=0

iii. Power rule:

d xndx=  n xn-1

iv. Product rule:

d (f*g)dx=f'*g+f*g'

2) Given:

xy=1+x2y

3) Calculations:

We have,

xy=1+x2y

Differentiate with respect to x,

ddxxy=ddx(1+x2y)

Apply Chan rule on left side

12xyddx(xy)=ddx(1+x2y)

Apply product rule of differentiation on left side, and apply Sum and difference rule on right side,

12xyyddxx+xddx(y)=ddx(1)+ddx(x2y)

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