   Chapter 11.3, Problem 5E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-6, find d y / d x at the given point without first solving for y. x 2 + 3 x y − 4 = 0  at (1,1)

To determine

To calculate: The value of dydx for the provided equation x2+3xy4=0 at (1,1).

Explanation

Given Information:

The provided equation is, x2+3xy4=0 and the provided point is (1,1).

Formula used:

When y is an implied function of x, obtain dydx by differentiating both sides of the equation with respect to x and then algebraically solve for dydx.

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

Calculation:

Consider the provided equation,

x2+3xy4=0

First, take the derivative of both sides of the equation with respect to x as,

ddx(x2+3xy4)=ddx(0)

To obtain the derivative by the use the product rule of derivatives as,

2x+3[yddx(x)+xddx(y)]0=02x+3[y1

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