Advertisements
Advertisements
प्रश्न
Find the derivative of x at x = 1.
उत्तर
Let f(x) = x Accordingly,
`f'(1) = lim_(h → 0)(f(1 + h) - f(1))/h`
= ` lim_(h → 0)((1 + h)- 1)/h`
= `lim_(h->0)h/h`
= `lim_(h->0)(1)`
= 1
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of `2/(x + 1) - x^2/(3x -1)`.
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 + a)
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):
`(1 + 1/x)/(1- 1/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):
`1/(ax^2 + bx + c)`
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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) x at x = 1
\[\frac{x^2 + 1}{x}\]
k xn
x2 + x + 3
\[\frac{2x + 3}{x - 2}\]
Differentiate each of the following from first principle:
e−x
x ex
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
ex log a + ea long x + ea log a
x3 ex
xn tan x
sin x cos x
sin2 x
\[e^x \log \sqrt{x} \tan x\]
x4 (5 sin x − 3 cos x)
(2x2 − 3) sin x
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
(ax + b)n (cx + d)n
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{x + \cos x}{\tan x}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of 2x4 + x.
