   Chapter 2.6, Problem 5E

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# Find d y / d x by implicit differentiation. x 2 − 4 x y + y 2 = 4

To determine

To find:

dy dx

by implicit differentiation.

Explanation

1) Formula:

i. Power rule:

d xndx=  n xn-1

ii. Product rule:

d (f*g)dx=f'*g+f*g'

iii. Constant rule:

d(c)dx=0

2) Given:

x2-4xy+ y2 =4

3) Calculations:

x2-4xy+ y2 =4

Use power rule to find derivative of x2 and y2, product rule for 4xy and constant rule for 4

2*x2-1-4xdydx+y+ 2* y2-1dydx =0

2x-4xdydx-4y+ 2ydydx =0

Combine like terms

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