Advertisements
Advertisements
प्रश्न
Find the derivative of f(x) = ax + b, where a and b are non-zero constants, by first principle
उत्तर
By definition,
f'(x) = `lim_(b -> 0) (f(x + h) - f(x))/h`
= `lim_(h -> 0) (a(x + h) + b - (ax + b))/h`
= `lim_(h -> 0) (bh)/h`
= b
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.
Find the derivative of `(x^n - a^n)/(x -a)` for some constant a.
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:
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^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/(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 `cosx/(1 + sinx)`
`(3x + 4)/(5x^2 - 7x + 9)`
`(x^5 - cosx)/sinx`
`(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 `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 ______.
If `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...,` then `(dy)/(dx)` = ______.
