Explanation Formula used: 1. d ( sin − 1 u ) d x = 1 1 − u 2 d u d x 2. d ( u ⋅ v ) d x = u d v d x + v d u d x Point slope formula. Let ( x 1 , y 1 ) be any point on the line and m be the slope of the line then the equation of the straight line is y − y 1 = m ( x − x 1 ) . Calculation: The given function is y = x sin − 1 x . Differentiate y = x sin − 1 x with respect to x , which is the slope of the curve. d y d x = d d x ( x sin − 1 x ) = x ⋅ 1 1 − x 2 + sin − 1 x ⋅ ( 1 ) = x 1 − x 2 + sin − 1 x Substitute x = 0.5 in d y d x = x 1 − x 2 + sin − 1 x . d y d x | x = 0

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Chapter 27.4, Problem 9E

To determine

The equation of the line tangent to the curve of y=xsin−1x at x=0.50.

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Chapter 27.4, Problem 8E

Chapter 27.4, Problem 10E

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Chapter 27 Solutions

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The equation of the line tangent to the curve of y = x sin − 1 x at x = 0.50 .

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