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36 votes
36 votes
Find the derivative of the function z = 3t^17/3 − 2t^9/4 − t^1/2 + 8

User Andreas Engedal
by
2.9k points

1 Answer

13 votes
13 votes

Answer:


\frac{-9x^{(7)/(4)}-1+34x^{(31)/(6)}}{2x^{(1)/(2)}}

Explanation:

first: we apply the sum-difference rule =
(d)/(dx)\left(3x^{(17)/(3)}\right)-(d)/(dx)\left(2x^{(9)/(4)}\right)-(d)/(dx)\left(x^{(1)/(2)}\right)+(d)/(dx)\left(8\right)

solve
(d)/(dx)\left(3x^{(17)/(3)}\right) =
((17)/(3))(3^((17)/(3)-1) =
17x^ (14)/(3)

solve
(d)/(dx)\left(2x^{(9)/(4)}\right) =
((9)/(4))(2x^(9)/(4)^-^1) =
(9)/(2)x^((5)/(4))

solve
(d)/(dx)\left(x^{(1)/(2)}\right) =
(1)/(2√(x) )

solve
(d)/(dx)\left(8\right) = 0

combine the answers:
= 17x^{(14)/(3)}-\frac{9x^{(5)/(4)}}{2}-\frac{1}{2x^{(1)/(2)}}+0

simplify:
\frac{-9x^{(7)/(4)}-1+34x^{(31)/(6)}}{2x^{(1)/(2)}}

User Aruna Karunarathna
by
2.9k points