Advertisements
Advertisements
प्रश्न
If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to ______.
विकल्प
`1/100`
100
does not exist
0
उत्तर
If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to 100.
Explanation:
Given `f(x) = 1 + x + x^2/2 + ... + x^100/100`
`f"'"(x) = 1 + (2x)/2 + ... + (100x^99)/100`
∴ `f""(1)` = 1 + 1 + ... + 1 (100 times) = 100
APPEARS IN
संबंधित प्रश्न
Find the derivative of `x^n + ax^(n-1) + a^2 x^(n-2) + ...+ a^(n -1) x + a^n` for some fixed real number a.
Find the derivative of `(x^n - a^n)/(x -a)` for some constant a.
Find the derivative of the following function.
sin x cos x
Find the derivative of the following function:
sec x
Find the derivative of the following function:
cosec x
Find the derivative of the following function:
5sin x – 6cos x + 7
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
(ax2 + sin x) (p + q cos x)
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`(x^2 cos (pi/4))/sin x`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`x/(1 + tan x)`
Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):
`x/(sin^n x)`
Find the derivative of f(x) = x3, by first principle.
Find the derivative of `cosx/(1 + sinx)`
`(x^4 + x^3 + x^2 + 1)/x`
`(x + 1/x)^3`
`(3x + 4)/(5x^2 - 7x + 9)`
x2 sin x + cos 2x
sin3x cos3x
If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is ______.
if `f(x) = (x - 4)/(2sqrt(x))`, then f'(1) is ______.
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is ______.
If `f(x) = x^100 + x^99 .... + x + 1`, then f'(1) is equal to ______.
