Home
Class 12
MATHS
Find the derivative of (x+3)^2(x+4)^3(x+...

Find the derivative of `(x+3)^2(x+4)^3(x+5)^4` w.r.t. `x`

Text Solution

Verified by Experts

`"Let "y = (x + 3)^(2) * (x + 4)^(3) * (x + 5)^(4)`
`"log "y ="log "{(x + 3)^(2)(x + 4)^(3)(x + 5)^(4)}`
`= 2 "log" (x+3) + 3 "log" (x+4) + 4"log" (x+5)`
Differentiate both sides w.r.t.x
`(1)/(y)(dy)/(dx)= (2)/(x+3)+(3)/(x+4)+(4)/(x+5)`
`rArr (dy)/(dx) = y [(2)/(x+3)+(3)/(x+4) + (4)/(x+5)]`
`rArr (dy)/(dx) = (x+3)^(2)(x+4)^(3)(x+5)^(4)[(2)/(x+3) + (3)/(x+4) + (4)/(x+5)]`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.6|11 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.7|17 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5.4|10 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

Find the derivative of y=x^(1/x)+(sin x)^(1/x) w.r.t. x

Find the derivative of (2x^(3)+3)(x^(2)+4) w.r.t x

Find the derivative of (4+x^(2))e^(2x) w.r.t to x .

Find the derivative of 7^(x) w.r.t x^(7).

The derivative of f(x)= 3x^2 +2x + 4 w.r.t. x is

Find derivative of cos x^(3).sin^(2)(x^(5)) w.r.t.to x

Find the derivative of |x^(2)+2| w.r.t.x.

Find the derivative of (x^(3) - 3x^(2) + 4)(4x^(5) + x^(2) -1) :

Find the derivative of (log x)^(cos x) w.r.t.x

Find the derivative of e^(x)(x^(2)+1) w.r.t. x