Question

Differential of log [log (log x⁵)] w.r.t x is ______.

Options

• `5/(xlog(x^5)log(logx^5)`

• `5/(xlog(logx^5)`

• `(5x^4)/(log(x^5)log(logx^5)`

• `(5x^4)/(logx^5log(logx^5)`

Answer 1

Differential of log [log (log x⁵)] w.r.t x is `underlinebb(5/(xlog(x^5)log(logx^5))`.

Explanation:

Let `y = log[log(logx^5)]`

∴ `d/dx = 1/(log(logx^5)) d/dx [log(logx^5)]`  ...(By Chain Rule)

= `1/(log(logx^5)) * 1/(logx^5) d/dx logx^5`

= `1/(log(x^5)log(logx^5)) 1/x^5 d/dx (x^5)`

= `5/(xlog(x^5)log(logx^5)`