Advertisements
Advertisements
Question
`(3x + 4)/(5x^2 - 7x + 9)`
Solution
`d/(dx) ((3x + 4)/(5x^2 - 7x + 9))`
= `((5x^2 - 9x + 9) d/(dx) (3x + 4) - (3x + 4) * d/(dx) (5x^2 - 7x + 9))/(5x^2 - 7x + 9)^2` .....[Using quotient rule]
= `((5x^2 - 7x + 9)(3) - (3x + 4)(10x - 7))/(5x^2 - 7x + 9)^2`
= `(15x^2 - 21x + 27 - 30x^2 + 21x - 40x + 28)/(5x^2 - 7x + 9)^2`
= `(-15x^2 - 40x + 55)/(5x^2 - 7x + 9)^2`
= `(55 - 40x - 15x^2)/(5x^2 - 7x + 9)^2`
APPEARS IN
RELATED QUESTIONS
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.
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 (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):
`(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/(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 f(x) = `1/x` by first principle.
Find the derivative of `cosx/(1 + sinx)`
`(x^4 + x^3 + x^2 + 1)/x`
(sin x + cos x)2
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 = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` 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 ______.
