Explanation d 2 y d x 2 is the second derivative of y with respect to x Given: x = cos θ , y = sin θ , is parametric form of the curve y = f ( x ) , where θ is the parameter. Formula used: d 2 y d x 2 = x ' ( θ ) y ' ( θ ) − y ' ( θ ) x ' ' ( θ ) ( x ' ( θ ) ) 3 --------------------- (i) d d θ ( cos θ ) = − sin θ ------------------- (ii) d d θ ( sin θ ) = cos θ --------------------- (iii) ( A B ) n = A n B n d d x ( f ( x ) ) = 1 2 f ( x ) ⋅ d d x ( f ( x ) ) Calculation: Where x ' ( θ ) = d x ( θ ) d θ = d d θ ( cos θ ) = − sin θ , [using (iii)] x " ( θ ) = d 2 x ( θ ) d θ 2 = d d θ ( x ' ( θ ) ) = = d d θ ( − sin θ ) = = − d d θ ( sin θ ) = − cos θ , [using (ii)] y ' ( θ ) = d y ( θ ) d θ y ' ( θ ) = d y ( θ ) d θ = d d θ ( sin θ ) = cos θ , [using (ii)] y ' ( θ ) = cos θ y ' ' ( θ ) = d 2 y ( θ ) d θ 2 y ' ' ( θ ) = d 2 y (

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.1, Problem 94E

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$\frac{d^{2} y}{d x^{2}}$

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Chapter 12.1, Problem 93E

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d 2 y d x 2

Solution Summary: The author explains how the second derivative of y with respect to x is d2ydx2, where is the parameter.

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$\frac{d^{2} y}{d x^{2}}$