Advertisements
Advertisements
प्रश्न
Find the derivative of f(x) = `1/x` by first principle.
उत्तर
By definition,
f'(x) = `lim_(h -> 0) (f(x + h) - f(x))/h`
= `lim_(h -> 0) 1/h 1/(x + h) - 1/x`
= `lim_(h -> 0) (-h)/(h(x + h)x)`
= `(-1)/x^2`.
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.
Find the derivative of the following function.
sin x cos x
Find the derivative of the following function:
5sin x – 6cos x + 7
Find the derivative of the following function:
2tan x – 7sec 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):
(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 + sec x) (x – tan 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) = sin x, by first principle.
Find the derivative of `cosx/(1 + sinx)`
`(x + 1/x)^3`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^5 - cosx)/sinx`
(2x – 7)2 (3x + 5)3
sin3x cos3x
If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is ______.
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is ______.
If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to ______.
If `f(x) = x^100 + x^99 .... + x + 1`, then f'(1) is equal to ______.
If `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...,` then `(dy)/(dx)` = ______.
