Advertisements
Advertisements
प्रश्न
If `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...,` then `(dy)/(dx)` = ______.
उत्तर
Given that `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...`
`(dy)/(dx) = 0 + 1/(1!) + (2x)/(2!) + (3x^2)/(31) + ...`
= `1 + x/(1!) + x^2/(2!) + x^3/(31) + ...`
= y
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.
For some constants a and b, find the derivative of (ax2 + b)2.
For some constants a and b, find the derivative of `(x - a)/(x - b)`.
Find the derivative of `(x^n - a^n)/(x -a)` for some constant a.
Find the derivative of cos x from first principle.
Find the derivative of the following function:
3cot x + 5cosec 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):
`(4x + 5sin x)/(3x + 7cos 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 + sec x) (x – 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) = ax2 + bx + c, where a, b and c are none-zero constant, by first principle.
Find the derivative of f(x) = x3, by first principle.
Find the derivative of f(x) = `1/x` by first principle.
Find the derivative of f(x) = sin x, by first principle.
`(x + 1/x)^3`
`(x^5 - cosx)/sinx`
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 `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to ______.
If `f(x) = 1 - x + x^2 - x^3 + ... -x^99 + x^100`, then f'(1) is equal to ______.
