हिंदी

Find the derivative of x at x = 1.

Advertisements
Advertisements

प्रश्न

Find the derivative of x at x = 1.

योग
Advertisements

उत्तर

Let f(x) = x Accordingly,

`f'(1) = lim_(h → 0)(f(1 + h) - f(1))/h`

= ` lim_(h → 0)((1 + h)- 1)/h`

= `lim_(h->0)h/h`

= `lim_(h->0)(1)`

= 1

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Limits and Derivatives - EXERCISE 12.2 [पृष्ठ २४८]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
अध्याय 12 Limits and Derivatives
EXERCISE 12.2 | Q 2. | पृष्ठ २४८

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the derivative of x2 – 2 at x = 10.


Find the derivative of (5x3 + 3x – 1) (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):

`(1 + 1/x)/(1- 1/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):

`(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):

`(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 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) = cos x at x = 0


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


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


\[\frac{1}{\sqrt{x}}\]


k xn


 x2 + x + 3


(x + 2)3


 (x2 + 1) (x − 5)


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


Differentiate each of the following from first principle: 

\[\frac{\cos x}{x}\]


3x + x3 + 33


\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]


 log3 x + 3 loge x + 2 tan x


\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]  


x−3 (5 + 3x) 


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. 


\[\frac{x + e^x}{1 + \log x}\] 


\[\frac{x \tan x}{\sec x + \tan x}\]


\[\frac{x^2 - x + 1}{x^2 + x + 1}\] 


\[\frac{a + \sin x}{1 + a \sin x}\] 


\[\frac{{10}^x}{\sin x}\] 


\[\frac{3^x}{x + \tan x}\] 


\[\frac{x^5 - \cos x}{\sin x}\] 


\[\frac{x}{\sin^n x}\]


\[\frac{ax + b}{p x^2 + qx + r}\] 


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


`(a + b sin x)/(c + d cos x)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×