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):
(ax2 + sin x) (p + q cos x)
उत्तर
(uv)' = u'v + uv'
∴ `d/dx[(ax^2 + sin x)(p + q cos x)]`
= `[d/dx (ax^2 + sin x)](p + q cos x) + (ax^2 + sin x) d/dx (p + q cos x)`
= (2ax + cos x)(p + q cos x) + (ax2 + sin x)(−q sin x)
= (−q sin x) (ax2 + sin x) + (p + q cos x) (2ax + cos x)
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 cos x from first principle.
Find the derivative of the following function.
sin x cos x
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:
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):
(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/(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) = ax2 + bx + c, where a, b and c are none-zero constant, by first principle.
Find the derivative of f(x) = `1/x` by first principle.
Find the derivative of f(x) = sin x, by first principle.
Find the derivative of `cosx/(1 + sinx)`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^2 cos pi/4)/sinx`
(sin x + cos x)2
(2x – 7)2 (3x + 5)3
x2 sin x + cos 2x
sin3x cos3x
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 `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 ______.
