`e^(x) log_(a) x` का x के सापेक्ष अवलन गुणांक ज्ञात कीजिये ।

Explanation

`y=e^(x) log_(a) x `
या `y=e^(x)log_(e)x log_(a)e`
या `(dy)/(dx)=log_(a)e(d)/(dx)(underset(I)e^(x) underset(II)(log_(e)x))`
`=log_(a)e[e^(x).(1)/(x)+e^(x)log_(e)x]`
`=e^(x)log_(a)e[(1)/(x)+log_(e)x]`
`e^(x)log_(a)e+e^(x)log_(e)xlog_(a)e`
`=(e^(x))/(x)log_(a)e + e^(x)log_(a)x`
`=e^(x)[(log_(a)e)/(x)+log_(a)x]`