2. D8: I can compute derivatives using multiple rules in combination. D9: I can compute derivativesof implicitly defined functions.(a) You are a tutor in the calculus center and three students come to you with questions aboutd- cos(xy). How would you help these students find and learn from their mistakes? (Youmay wish to reference the rubrics above to help identify mistakes.)dxHugh Manatee's answer:dcos(xy) = sin(y + x)dxii. Bob:i. Hugh: sin(xy) (y + x-iii. Dee:Dee Rivative's answer:ddx(b) Emboldened by your thoughtful assistance, Hugh, Dee and Bob give their final answers tothe problem below. Decide which answer, if any, is correct and briefly explain why.dyFind given that cos(xy) = sin (ln(y)) with y > 0.dxdydxdydxcos(xy)= sin(xy) (y + x)dy(v + adv)dxsin(xy)yx − cos(ln(y))1 dyy dxcos (ln(y)).sin(xy)y- sin(xy)x - cos (ln(y))Bob the Iguana's answer:ddxcos(ry) = − sin(ry) (1)

a) d(cosxy)/dxb) cos(xy)=sin(lny)

2. D8: I can compute derivatives using multiple rules in combination. D9: I can compute derivatives of implicitly defined functions. (a) You are a tutor in the calculus center and three students come to you with questions about d cos(xy). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.) dx Hugh Manatee's answer: d cos(xy) = sin(y + x) dx (b) Emboldened by your thoughtful assistance, Hugh, Dee and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why. dy Find given that cos(xy) = sin(ln(y)) with y > 0. dx i. Hugh: sin(xy) (y + x- dy dx ii. Bob: iii. Dee: Dee Rivative's answer: dx cos(xy) = sin(xy) (y + x) dx dy dx sin (cy)y x-cos(ln(y)) 1 dy y dx cos(ln(y)); sin(xy)y - sin(xy)x - cos (ln(y)) Bob the Iguana's answer: cos(xy) = sin(xy) (1) d dx dx

2. D8: I can compute derivatives using multiple rules in combination. D9: I can compute derivatives of implicitly defined functions. (a) You are a tutor in the calculus center and three students come to you with questions about d cos(xy). How would you help these students find and learn from their mistakes? (You may wish to reference the rubrics above to help identify mistakes.) dx Hugh Manatee's answer: d cos(xy) = sin(y + x) dx (b) Emboldened by your thoughtful assistance, Hugh, Dee and Bob give their final answers to the problem below. Decide which answer, if any, is correct and briefly explain why. dy Find given that cos(xy) = sin(ln(y)) with y > 0. dx i. Hugh: sin(xy) (y + x- dy dx ii. Bob: iii. Dee: Dee Rivative's answer: dx cos(xy) = sin(xy) (y + x) dx dy dx sin (cy)y x-cos(ln(y)) 1 dy y dx cos(ln(y)); sin(xy)y - sin(xy)x - cos (ln(y)) Bob the Iguana's answer: cos(xy) = sin(xy) (1) d dx dx

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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