Home
Class 12
MATHS
Find (dy)/(dx)fory=x^xdot...

Find `(dy)/(dx)fory=x^xdot`

Text Solution

Verified by Experts

The correct Answer is:
`x^(x)(1+ log x)`
`"Let "y=x^(x). Then, y= e^(xlog x).`
Differentiating both sides w.r.t. x, we get
`(dy)/(dx)=e^(x log x)(d)/(dx)(x log x)`
`=x^(x)(log x+ x(1)/(x))" "[becausee^(x log x)=x^(x)]`
`=x^(x)(1+ log x)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.6|8 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.7|6 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.4|10 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

Find (dy)/(dx) for y=x^(x)

Find (dy)/(dx) for y=x^(x)

Find (dy)/(dx) of y=x^(x^(x))

Find (dy)/(dx) if y=2^(x^(x))

Find (dy)/(dx) if y^(x)=x^(y)

Find (dy)/(dx) , if y=e^(x^(3))

Find (dy)/(dx) ,if y=e^(x^(3)) ?

FInd (dy)/(dx) of y=sin^3x

Find, dy/dx if y = x^x