   Chapter 11.3, Problem 25E ### 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

# For Problems 23-26, find the slope of the line tangent to the curve. x 2 + 2 x y   + 3 = 0  at (1, 2)

To determine

To calculate: The slope of the tangent line to the curve x2+2xy+3=0 at (1,2).

Explanation

Given Information:

The provided equation of the curve is, x2+2xy+3=0 and the point is (1,2).

Formula used:

The slope of tangent to a curve y=f(x) at point (x,y) is given by the derivative of the curve at that point.

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

Calculation:

Consider the provided equation of curve,

x2+2xy+3=0

Now, find the derivative dydx from x2+2xy+3=0 by taking the derivative term by term on both sides of the equation as,

ddx(x2)+ddx(2xy)+ddx(3)=ddx(0)

Now, use the product rule,

ddx(uv

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