Advertisements
Advertisements
प्रश्न
(sin x + cos x)2
उत्तर
`d/(dx) (sinx + cosx)^2 = d/(dx) (sinx + cosx)(sinx + cosx)`
= `(sin x + cosx) d/(dx) (sin x + cosx) + (sin x + cosx) d/(dx) (sin x + cosx)`
= `2(sinx + cosx) d/(dx) (sinx + cosx)`
= `2(sinx + cosx)(cosx - sin x)`
= `2(cos^2x - sin^2x)`
= `2 cos^2x`
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 `(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:
cosec 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 + 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) = 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^4 + x^3 + x^2 + 1)/x`
`(x^2 cos pi/4)/sinx`
(2x – 7)2 (3x + 5)3
x2 sin x + cos 2x
sin3x cos3x
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 `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 ______.
