If `t=(5^(x))/(x^(5))`, find `(dy)/(dx).`

1.	If `t=(5^(x))/(x^(5))`, find `(dy)/(dx).`
Answer» Given : `y=(5^(x))/(x^(5))." …(i)"` Taking logarithm on both sides of (i), we get `logy=log(5^(x))-log(x^(5))` `rArr log y = x log 5-5log x` `rArr(1)/(y).(dy)/(dx)=(log5).1-(5)/(x)" [differentiating both sides w.r.t.x]"` `rArr(dy)/(dx)=y(log5-(5)/(x))` `rArr(dy)/(dx)=(5^(x))/(x^(5))(log5-(5)/(x)).`

Discussion

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