यदि log[log{log(x)}] = y है, तो \(\rm \frac{{dy}}{{dx}}\) का मान ज्ञात करें।

गणना:

दिया हुआ है कि:

y = log[log{log(x)}] 

x के संबंध में अवकलन करने पर

⇒ \(\rm \frac{{dy}}{{dx}} =\frac {d \;log[log{log(x)}] }{dx}\)

\(\rm =\frac {d \log[\log{\log(x)}] }{d\log{\log(x)}} \times \frac {d\log{\log(x)}}{dx}\)

\(\rm =\frac {d \log[\log{\log(x)}] }{d\log{\log(x)}} \times \frac {d\log{\log(x)}}{d\log x} \times \frac {d \log x}{dx}\)

\(\rm = \left( {\frac{1}{{\left[ {\log \left\{ {\log \left( x \right)} \right\}} \right]}}} \right) \times \;\left( {\frac{1}{{logx}}} \right) \times \left( {\frac{1}{x}} \right)\)

\(\rm \frac{{dy}}{{dx}}{\rm{\;}} = \left( {\frac{1}{{\left[ {\left( x \right)\left( {logx} \right)\log \left\{ {\log \left( x \right)} \right\}} \right]}}} \right)\)