Differentiate `(5x^(1//7)+(3)/(x^(3//2)))` with respect to `x`.

Options

A. `(5)/(7).x^(-5//7)-(9)/(7)x^(-5//2)`
B. `(5)/(7).x^(-5//8)-(9)/(2)x^(-5//2)`
C. `(5)/(7).x^(-5//7)-(9)/(2)x^(-5//2)`
D. `(5)/(7).x^(-6//7)-(9)/(2)x^(-5//2)`

Answer

D

Explanation

`(d)/(dx)(5x^1//7)+(3)/(x^(3//2)))`
`=5.(d)/(Dx)(x^(1//7))+3.(d)/(dx)(x^(-3//2))`
`=5.(1)/(7)x^(-6//7)+3.((-3)/(2)).x^( -5//2)`
`=(5)/(7).x^(-6//7)-(9)/(2)x^(-5//2)`