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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

4x2-y2=9

Short Answer

Expert verified

dydx=4xy

Step by step solution

01

Step 1. Given Information:

Given equation: 4x2-y2=9

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(4x2-y2)=ddx(9)ddx4x2-ddxy2=ddx98x-2y·dydx=02y·dydx=8xdydx=8x2ydydx=4xy

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