Question 1. compute the first derivative F(x) 2×5 + x3/2 – 1/2x
answer is f(x) = 10×4 – 3/2×1/2 + 1/2×2, 40×3 + 3/3×1/2 – 1/x3, – 120×2 – 3/8x – 3/2 + 3/x4
question 2. use leibnitz theorem to evalute the fourth derivative of (2×3 + 3×2 +x +2 )e2x
answer is 16(2×3 + 15×2 + 31x + 19)e2x
Question 3. find the total differential of function f(x,y) = yex+y
answer is df = [yex+y]dx + [(1+y) ex+y ]dy
Question 4. obtain the n-th differential coefficient of y = (x2+1)ex2
answer is 2n-2e2x (4×2+4nx + n2 – n +4)
Question 5. compute the third derivative of sinxInx using leibnitz theorem
Question 6. find the total differential of the function f(x,y) = x2 + 3xy with respect to x, given that y = sin-1x
answer is 2x + 3sin-1x + 3x/(1+x2)1/2
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