Home
Class 11
MATHS
Find the derivative of x^n+a x^(n-1)1+a^...

Find the derivative of `x^n+a x^(n-1)1+a^2x^(n-2)+dotdotdot+a^(n-1)x+a^n`for some fixed real number a.

Text Solution

Verified by Experts

Let `y=x^(n)+ax^(n-1)+a^(2)x^(n-2)+.....+a^(n=1)x+a^(n)`
`rArr (dy)/(dx)=(d)/(dx)[x^(n)+ax^(n-1)+a^(2)x^(n-2)+.......+a^(n-1)x+a^(n)]`
`=(d)/(dx)x^(n)+a(d)/(dx)x^(n-1)+a^(2)(d)/(dx)x^(n-2)+.........+a^(n-1)(d)/(dx)x+(d)/(dx)a^(n)`
`=nx^(n-1)+a(n-1)x^(n- 2)+a^(2)(n-2)x^(n-3)`
`+..........+a^(n-1).1+0`
`=nx^(n-1)+a(n-1)x^(n-2)+a^(2)(n-2)x^(n-3)+.....+a^(n-1)`.
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|30 Videos

  • LIMITS AND DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise EX -13.1|32 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|6 Videos

  • LINEAR INEQUALITIES

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|14 Videos

Similar Questions

Explore conceptually related problems

Find the derivative of (x^n-a^n)/(x-a) for some constant a.

Find the derivative of (x^(n)-a^(n))/(x-a) at x=a for some constant a.

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiation.

Find the coefficient of x^n in (1+x/(1!)+(x^2)/(2!)+........+(x^n)/(n !))^2 .

If a\ a n d\ b are the coefficients of x^n in the expansions of (1+x)^(2n) and (1+x)^(2n-1) respectively, find a/b .

The coefficients fo x^(n) in the expansion of (1+x)^(2n) and (1+x)^(2n-1) are in the ratio

If A and B are the coefficients of x^n in the expansion (1 + x)^(2n) and (1 + x)^(2n-1) respectively, then A/B is

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.

Given that bar x is the mean and sigma^2 is the variance of n observations x_1x_2 , ..., x_n . Prove that the mean and variance of the observations a x_1,a x_2 , a x_3,dotdotdot,a x_n are a bar x and a^2sigma^2 ,