Question

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

Answer 1

`\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)}}`