   Chapter 11.3, Problem 35E ### 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

# Find the slope of the tangent to the curve y 2 ln  x + x 2 y =   3 at the point (1, 3).

To determine

To calculate: The slope of the tangent line to the curve y2lnx+x2y=3 at (1,3).

Explanation

Given Information:

The provided equation of the curve is, y2lnx+x2y=3 and point is (1,3).

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,

y2lnx+x2y=3

Now, find the derivative dydx from y2lnx+x2y=3 by taking the derivative term by term on both sides of the equation as,

ddx(y2lnx)+ddx(x2y)=ddx(3)

Now, use the product rule,

ddx(uv)=udvdx+vdudx

To obtain the derivative of y2lnx and x2y as,

y2ddx(lnx)+lnxddx(y2)+yddx

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