Advertisements
Advertisements
प्रश्न
Find the derivative of 99x at x = 100.
Advertisements
उत्तर
`f'(a) = lim_(x → a) (f(a + h) - f(a))/h`
`f'(100) = lim_(h → 0) (99 (100 + h) - 99 xx 100)/h`
= ` lim_(h → 0) (99 xx 100 + 99h - 99 xx 100)/h`
= `= lim_(h → 0)(99 xx h)/h`
= 99
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–4 (3 – 4x–5).
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):
`a/x^4 = b/x^2 + 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):
`(sec x - 1)/(sec x + 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):
`(sin(x + a))/ 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
k xn
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
log3 x + 3 loge x + 2 tan x
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
cos (x + a)
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
x3 sin x
x3 ex
xn loga x
(x3 + x2 + 1) sin x
x5 ex + x6 log x
(1 +x2) cos x
x4 (5 sin x − 3 cos x)
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{1 + \log x}{1 - \log x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of 2x4 + x.
`(a + b sin x)/(c + d cos x)`
