Home
Class 12
MATHS
differentiate: log(logx)...

differentiate: log(logx)

Text Solution

Verified by Experts

Let `y="log"("log"x)`
`implies(dy)/(dx)=(d)/(dx)"log"("log"x)`
`=(1)/("log"x)(d)/(dx)("log"x)`
`=(1)/(x"log"x)=(x log x)^(-1)`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)(x log x)^(-1)`
`= -1* (x logx)^(-2)(d)/(dx)(x logx)`
`=([x*(d)/(dx)logx+"log"x(d)/(dx)x])/((xlogx)^(2))`
`=([x*(1)/(x)+"log"x])/((xlogx)^(2))`
`=((1+"log"x))/((xlogx)^(2))`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.8|6 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.6|11 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

differentiate: log(log x)

Differentiate log[log(logx)] w.r.t. x.

Differentiate : log{log[log(x^(4))]}

Differentiate log (7 log x) w.r.t.x

Differentiate: (log x)^(x)+x^(log x) with respect to x:

Differentiate: (log x)^(x)+x^(log x) with respect to x.

Differentiate log[log(logx^(5))]

Differentiate : (log(cos x))/(tan(log x))

Differentiate (log x)^(x) with respect to log x

Differentiate (log x)^(x) with respect to log x