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 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):
`(a + bsin x)/(c + dcosx)`
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) x at x = 1
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
k xn
(x + 2)3
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
sin x + cos x
tan 2x
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
xn loga x
(1 +x2) cos x
x4 (5 sin x − 3 cos x)
x−3 (5 + 3x)
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)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
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.
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
