Advertisements
Advertisements
Question
If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is ______.
Options
`(-4x)/(x^2 - 1)^2`
`(-4x)/(x^2 - 1)`
`(1 - x^2)/(4x)`
`(4x)/(x^2 - 1)`
Advertisements
Solution
If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is `(-4x)/(x^2 - 1)^2`.
Explanation:
Given `y = (1 + 1/x^2)/(1 - 1/x^2)`
⇒ `y = (x^2 + 1)/(x^2 - 1)`
∴ `(dy)/(dx) = ((x^2 - 1) * 2x - (x^2 + 1) * 2x)/(x^2 - 1)^2`
= `(2x(x^2 - 1 - x^2 - 1))/(x62 - 1)^2`
= `(2x(-2))/(x^2 - 1)^2`
= `(-4x)/(x^2 - 1)^2`
APPEARS IN
RELATED QUESTIONS
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:
5 sec x + 4 cos x
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):
(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):
(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/(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) = ax + b, where a and b are non-zero constants, by first principle
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) = sin x, 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)`
`(x^5 - cosx)/sinx`
(sin x + cos x)2
(2x – 7)2 (3x + 5)3
x2 sin x + cos 2x
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 + 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) = 1 - x + x^2 - x^3 + ... -x^99 + x^100`, then f'(1) is equal to ______.
