Advertisements
Advertisements
प्रश्न
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is ______.
विकल्प
cos 9
sin 9
0
1
Advertisements
उत्तर
If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is cos 9.
Explanation:
Given `y = (sin(x + 9))/cosx`
`(dy)/(dx) = (cosx * cos(x + 9) - sin(x + 9)(- sin x))/(cos^2x)`
= `(cos x cos(x + 9) + sin x sin(x + 9))/(cos^x)`
= `(cos(x + 9 - x))/(cos^2x)`
= `cos9/(cos^2x)`
∴ `((dy)/(dx))_("at" x = 0) = cos9/(cos^2 0)`
= `cos9/(1)^2`
= cos 9
APPEARS IN
संबंधित प्रश्न
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 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:
3cot x + 5cosec 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/(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) = x3, by first principle.
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`
`(x + 1/x)^3`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^5 - cosx)/sinx`
`(x^2 cos pi/4)/sinx`
(sin x + cos x)2
x2 sin x + cos 2x
If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is ______.
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 `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 ______.
