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y=2(t+1)(t-1) plz i need the differentiation for this2. x=3t(t+1)(t^2+1)3. x=(3t^2+4t-1)/t^2

y=2(t+1)(t-1) plz i need the differentiation for this2. x=3t(t+1)(t^2+1)3. x=(3t^2+4t-1)/t^2

Grade:11

1 Answers

sonika p
129 Points
3 years ago
using multiplication rule, d(uv) = vdu + udv
y = 2(t+1)(t-1)
dy/dt = 2[(t-1)(1) + (t+1)(1)] = 2[t-1 + t+1] = 2[2t] = 4t
 
x = 3t(t+1)(t2 +1)
dx/dt = 3[t(t+1)(2t) + t(t2+1)(1) + (t+1)(t2+1)] = 3[2t^3 + 2t^2 + t^3 +t + t^3 +t^2 +t+1] = 3[4t^3 + 3t^2 +2t +1]
= 12t^3 + 9t^2 +6t +3
 
x=(3t^2+4t-1)/t^2 = 3 + 4/t – 1/t^2 = -4/t^2 + 2/t^3

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