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91Ó°ÊÓ

Each of the equations in Exercises 69–80 defines y as an implicit function of x. Use implicit differentiation (without solving for y first) to find dydx

x2+y2=4

Short Answer

Expert verified

dydx=-xy

Step by step solution

01

Step 1. Given Information:

Given equation: x2+y2=4

We want to find dydxdefines y as an implicit function of x by use implicit differentiation.

02

Step 2. Solution:

Differentiate both sides w.r.t. x

ddx(x2+y2)=ddx(4)ddxx2+ddxy2=ddx42x+2y·dydx=02y·dydx=-2xdydx=-2x2ydydx=-xy

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