Advertisements
Advertisements
प्रश्न
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)`
Advertisements
उत्तर
`d/dx(u/v) = (uv - uv)/v^2`
`d/dx((4x + 5sin x)/(3x + 7 cos x)) = ([d/dx(4x + 5sin x)](3x + 7 cos x) - (4" + 5 sin x) d/dx(3x + 7 cos x))/(3x + 7 cos x)^2`
= `((4 + 5 cos x)(3x + 7 cos x) - (4x + 5 sin x)(3 - 7 sin x))/(3x + 7 cos x)^2`
= `((12x + 28 cos x + 15x cos x + 35 cos^2 x) - (12x - 28x sin x + 15 sin x - 35 sin^2 x))/(3x + 7 cos x)^2`
= `(28(cos x + x sin x) + 15(x cos x - sin x) + 35 (cos^2 x + sin ^2 x))/(3x + 7 cos x)^2`
= `(35 + 15xcos x + 28 cos x + 28 x sin x - 15 sin x)/((3x + 7 cos 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 (x – a) (x – b).
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.
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:
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):
(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/(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) = x3, by first principle.
Find the derivative of f(x) = sin x, by first principle.
`(x + 1/x)^3`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^5 - cosx)/sinx`
(sin x + cos x)2
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) = 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 ______.
