Advertisements
Advertisements
प्रश्न
Find the derivative of x at x = 1.
Advertisements
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 `2x - 3/4`
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x–3 (5 + 3x).
Find the derivative of x5 (3 – 6x–9).
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):
`(px^2 +qx + r)/(ax +b)`
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):
cosec x cot x
Find the derivative of f (x) = cos x at x = 0
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
x2 ex
\[\cos \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 ex
xn tan x
x2 sin x log x
(1 +x2) cos x
x3 ex cos x
(2x2 − 3) sin x
x−4 (3 − 4x−5)
x−3 (5 + 3x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
