Advertisements
Advertisements
प्रश्न
Find the derivative of x2 – 2 at x = 10.
Advertisements
उत्तर
= `lim_(h → 0)(f(a + h) - f(a))/h`
∴ Derivative of x2 − 2 at x = 10
= `lim_(h → 0) ([(10 + h)^2 - 2]- (10^2 - 2))/h`
= `lim_(h → 0) (100 + 20h + h^2 - 2 - 100 + 2)/h`
= `lim_(h → 0) (20h + h^2)/h`
= `lim_(h → 0) (20 + h)`
= 20
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
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):
`(ax + b)/(cx + d)`
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):
(ax + b)n
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):
sin (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):
`(sin x + cos x)/(sin x - 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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = 99x at x = 100
x2 + x + 3
\[\frac{2x + 3}{x - 2}\]
x ex
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
\[\tan \sqrt{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
2 sec x + 3 cot x − 4 tan x
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
sin2 x
\[e^x \log \sqrt{x} \tan x\]
x5 (3 − 6x−9)
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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of f(x) = tan(ax + b), by first principle.
