English

Find the derivative of 99x at x = 100.

Advertisements
Advertisements

Question

Find the derivative of 99x at x = 100.

Sum
Advertisements

Solution

`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

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Limits and Derivatives - EXERCISE 12.2 [Page 248]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 12 Limits and Derivatives
EXERCISE 12.2 | Q 3. | Page 248

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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)/(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):

`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):

`(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 the following function at the indicated point:

2 cos x at x =\[\frac{\pi}{2}\] 


Find the derivative of the following function at the indicated point: 

 sin 2x at x =\[\frac{\pi}{2}\]


\[\frac{2}{x}\]


\[\frac{x^2 + 1}{x}\]


 x2 + x + 3


x ex


Differentiate  of the following from first principle:

\[\cos\left( x - \frac{\pi}{8} \right)\]


\[\sin \sqrt{2x}\]


x4 − 2 sin x + 3 cos x


ex log a + ea long x + ea log a


\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\] 


\[\frac{a \cos x + b \sin x + c}{\sin x}\]


2 sec x + 3 cot x − 4 tan x


\[\frac{(x + 5)(2 x^2 - 1)}{x}\]


\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\] 


If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ. 


For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]

 

xn loga x 


(1 − 2 tan x) (5 + 4 sin x)


x3 ex cos x 


Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same. 


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)


(ax + b) (a + d)2


\[\frac{a + \sin x}{1 + a \sin x}\] 


\[\frac{3^x}{x + \tan x}\] 


\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]


\[\frac{\sec x - 1}{\sec x + 1}\] 


If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]


Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×