Advertisements
Advertisements
प्रश्न
If `y = (sin x + cos x)/(sin x - cos x)`, then `(dy)/(dx)` at x = 0 is ______.
पर्याय
–2
0
`1/2`
Does not exist
उत्तर
If `y = (sin x + cos x)/(sin x - cos x)`, then `(dy)/(dx)` at x = 0 is –2.
Explanation:
Given `y = (sinx + cosx)/(sinx - cosx)`
`(dy)/(dx) = ((sin x - cos x)(cos x - sin x) - (sin x + cos x)(cos x + sin x))/(sin x - cos x)^2`
= `(-(sin x - cos x)^2 - (sin x + cos x)^2)/(sin x - cos x)^2`
= `(-[sin^2x + cos^2x - 2 sinx cosx + sin^2x + cos^2x + 2 sinx cos x])/(sin x - cos x)62`
= `(-2)/(sin x - cos x)^2`
∴ `((dy)/(dx))_("at" x = 0) = (-2)/(sin 0 - cos 0)^2`
= `(-2)/(-1)^2`
= –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:
sec 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):
`(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 + 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 = (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) = x^100 + x^99 .... + x + 1`, then f'(1) is equal to ______.
