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find the differential of each function (CALCULUS HELP PLEASE)?

find the differential of each function please.y = s / (2+5s)and...y = u ( cos(u) )THANKS!
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3 Answers

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Dr. Juanita Wolff

Feb 20, 2025

Hello,y = s / (2+5s)dy = (ds(2+5s) - 5s ds_/(2 + 5s)^2 = (2ds +5sds -5sds)/(2 + 45s)^2Then dy = 2ds/(2+5s)^2 or (2/(2+5s)^2)ds y = u ( cos(u) )dy = du(cos(u)) + u(-sin(u))du = (cos(u) -u sin(u)) duHope This Helps!... Show More
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Dr. Juanita Wolff

Feb 20, 2025

for the first 1:y = 2/(2+5s)^2and second 1:y= u(-sin(u))x(cos (u))i hope thts right! x... Show More
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Dr. Juanita Wolff

Feb 20, 2025

y = s / (2+5s)Apply the Quotient Rule:dy /ds = [(2+5s)(1)-s(5)] / (2+5s)^2dy/ds = 2/(2+5s)^2dy = 2ds / (2+5s)^2--------------------------------------------------------y= u cos(u)dy/du = cos(u)-usin(u)dy = cos(u)du - usin(u)du... Show More
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