Question

differentiate the following w. r. t. x (log(log x))^6​

Answer 1

Answer:

$\\\tt \dfrac{6}{ x log(x^{6}) }$

Formula used :

$\\\tt \dfrac{dt}{dx} = \dfrac{dt}{dy} * \dfrac{dy}{dx} \ (chain\ rule)$

$\\\tt \dfrac{d log(x)}{dx} = \dfrac{1}{x}$

Steps:

$\\\tt \dfrac{d (log(log(x)^{6}))}{dx}$

$\\\tt \dfrac{d (log(log(x)^{6}))}{d(logx^{6})} * \dfrac{d(logx^{6}) } {d x^{6}} * \dfrac{d x^{6} } {d x}\\\\= \dfrac{1}{log(x)^{6}} * \dfrac{1}{x^{6}}* 6x^{5} \\= \dfrac{6}{ x log(x^{6}) }$