Advertisements
Advertisements
Question
(sin x + cos x)2
Advertisements
Solution
`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
RELATED QUESTIONS
For some constants a and b, find the derivative of (ax2 + b)2.
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):
`(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 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) = 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 f(x) = sin x, by first principle.
`(x^4 + x^3 + x^2 + 1)/x`
`(x + 1/x)^3`
`(x^5 - cosx)/sinx`
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 + cos x)/(sin x - cos x)`, then `(dy)/(dx)` at x = 0 is ______.
If `f(x) = 1 - x + x^2 - x^3 + ... -x^99 + x^100`, then f'(1) is equal to ______.
