Explanation Given Information: The provided equation of the curve is, y e x = y 2 + x − 2 and point is ( 0 , 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, d d x ( u ⋅ v ) = u d v d x + v d u d x Calculation: Consider the provided equation of curve, y e x = y 2 + x − 2 Now, find the derivative d y d x from y e x = y 2 + x − 2 by taking the derivative term by term on both sides of the equation as: d d x ( y e x ) = d d x ( y 2 ) + d d x ( x ) − d d x ( 2 ) Now, use the product rule, d d x ( u ⋅ v ) = u d v d x + v d u d x To obtain the derivative of y e x as, d d x ( y e x ) = d d x ( y 2 ) + d d x ( x ) −

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Chapter 11.3, Problem 43E

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To calculate: The slope of the tangent line to the curve yex=y2+x−2 at (0,2).

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Chapter 11.3, Problem 42E

Chapter 11.3, Problem 44E

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Chapter 11 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The slope of the tangent line to the curve y e x = y 2 + x − 2 at ( 0 , 2 ) .

Solution Summary: The author calculates the slope of the tangent line to the curve y=f(x,y) at the provided point.

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To calculate: The slope of the tangent line to the curve yex=y2+x−2 at (0,2).

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