MTH 151 Quiz: MATH151 Quiz 4 2017 Fall Solutions
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2(x3 + 1) 1/3 : suppose sin(x2 + y2) = xy. Use implicit di erentiation to write dy dx in terms of x and y: suppose ex+y = (x + y)2. Use implicit di erentiation to write dy dx in terms of x and y: lim x 0 sin2(2x) sin(3x2) Solutions d dx e1+sin2 x = e1+sin2(x) d dx (1 + sin2(x)) = e1+sin2(x) 2 sin(x) cos(x) (cid:16) e1+sin2(x)(cid:17) = 2x2(x3 + 1) 4/3 (x3 + 1) 4/3 d dx (x3 + 1) 4/3(3x2) (x3 + 1) (chain rule) (chain rule) (chain rule: suppose sin(x2 + y2) = xy. Di erentiate both sides of the given equation with respect to x and solve for dy dx : d dx cos(x2 + y2) (cid:18) (cid:19) d dx xy. = y + x sin(x2 + y2) = 2x + 2y dy dx dy dx dy dx. 2x cos(x2 + y2) + 2y cos(x2 + y2)
