Advertisements
Advertisements
प्रश्न
For some constants a and b, find the derivative of `(x - a)/(x - b)`.
Advertisements
उत्तर
Let f(x) = `(x - a)/(x - b)`
f(x) = `d/(dx) ((x - a)/(x - b))`
By quotient rule,
`f'(x) = ((x - a)d/dx(x - b) - (x - a) d/dx (x - b))/(x - b)^2`
= `(1.(x - b) - (x - a) xx 1)/(x - b)^2`
= `(x - b - x + a)/(x - b)^2`
= `(a - b)/(x - b)^2`
APPEARS IN
संबंधित प्रश्न
For some constants a and b, find the derivative of (x – a) (x – b).
For some constants a and b, find the derivative of (ax2 + b)2.
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.
sin x cos x
Find the derivative of the following function:
sec x
Find the derivative of the following function:
5 sec x + 4 cos 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:
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):
(x2 + 1) 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 + cos 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):
`(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 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 `cosx/(1 + sinx)`
`(x^4 + x^3 + x^2 + 1)/x`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^5 - cosx)/sinx`
`(x^2 cos pi/4)/sinx`
(2x – 7)2 (3x + 5)3
If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is ______.
If `y = (sin x + cos x)/(sin x - cos x)`, then `(dy)/(dx)` at x = 0 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 `f(x) = 1 - x + x^2 - x^3 + ... -x^99 + x^100`, then f'(1) is equal to ______.
