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MATH 41 Midterm: Stanford MATH 41 12exam2sol

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turquoisegnu128

7 Mar 2019

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Stanford University

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MATH - Mathematics

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1 sin2 z 2 sin z cos z = 2 cot z. We use the chain rule to di erentiate g: g (t) = 1 + (t 2)2 ( 2t 3) t4(1 + t 4) = 0. (c) h(x) = ( x)ln x (5 points) we take the natural logarithm of both sides: ln(h(x)) = ln(( x)ln x) = ln x ln( x) = (ln x)2. We can write the nal result as follows: h (x) = h(x) ln x x. 0 = d dx (xy2) d dx (ey) + d dx (x cos y) = y2 + x 2y y ey y + cos y + x ( sin y y ). We rearrange the terms involving y to obtain: Therefore y2 + cos y = 2xy y + ey y + x sin y y . This equivalent to 1 + x = 2, so x = 3.

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Related Questions

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