Advertisements
Advertisements
प्रश्न
Find the derivative of f (x) = 99x at x = 100
उत्तर
\[ = \lim_{h \to 0} \frac{99(100 + h) - 99(100)}{h}\]
\[ = \lim_{h \to 0} \frac{9900 + 99h - 9900}{h}\]
\[ = \lim_{h \to 0} \frac{99h}{h}\]
\[ = \lim_{h \to 0} 99\]
\[ = 99\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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):
`(ax + b)/(px^2 + qx + r)`
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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
(x2 + 1) (x − 5)
x ex
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
\[\cos \sqrt{x}\]
cos (x + a)
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 ex
(x3 + x2 + 1) sin x
x5 ex + x6 log x
(1 +x2) cos x
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Find the derivative of f(x) = tan(ax + b), by first principle.