यदि `y=(e^(x) tan x)/(x^(3))`, तब `(dy)/(dx)` का मान ज्ञात कीजिएः।

Answer

`e^(x)x^(-3)[sec^(2)x+tan x(1-3//x)]`

Explanation

`y=(e^(x)tan x)/(x^(3))=(e^(x)x^(-3))tan x`
`(dy)/(dx)=(d)/(dx)[(e^(x)x(-3)tan ]`
`=e^(x)x^(-3)sec^(2)x+tan x[e^(x)(d)/(dx)(x^(-3))+x^(-3)(d)/(dx)(e^(x))]`
`=e^(x)x^(-3)sec^(2)x+tan x[e^(x)(-3x^(-4))+x^(-3)e^(x)]`
`=e^(x)x^(-3)sec^(2)x+e^(x)x^(-3)tanx-3x^(-4)e^(x)tanx`