Question

Differenciate x^6 with respect to 1/√x

Answer 1

`DIFFERENTIATION \\ \\ \\ Let \: u \: = \: {x}^(6) \: \: \: and \: v = (1)/( √(x) ) \\ \\ Then \: , \: (du)/(dx) \: = \: 6 {x}^(5) \\ \\ and \: \: \: \: \: \: (dv)/(dx) \: \: = \: ( - 1)/(2x √(x) ) \\ \\ \\ Therefore \: , \\ \\ \\ (du)/(dv) \: = \: ( (du)/(dx) )/( (dv)/(dx) ) \: = \: \frac{6 {x}^(5) }{ ( - 1)/(2x √(x) ) } \\ \\ (du)/(dv) \: = \: ( (du)/(dx) )/( (dv)/(dx) ) \: = - 12 {x}^{ (13)/(2) } \\ \\ \\ (du)/(dv) \: = - 12 {x}^{ (13)/(2) } \: \: \: \: \: \: \: \: Ans.`