हिंदी

Find the Derivative of the Following Function at the Indicated Point:

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

x at x = 1 

\[\left( ii \right) \hspace{0.167em}\text{ We have }: \]
\[f'(x) = \lim_{h \to 0} \frac{f(1 + h) - f(1)}{h}\]
\[ = \lim_{h \to 0} \frac{1 + h - 1}{h}\]
\[ = \lim_{h \to 0} 1\]
\[ = 1\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 30: Derivatives - Exercise 30.1 [पृष्ठ ३]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 30 Derivatives
Exercise 30.1 | Q 7.2 | पृष्ठ ३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the derivative of `2x - 3/4`


Find the derivative of x–3 (5 + 3x).


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):

`4sqrtx - 2`


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):

cosec x cot 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 + cos x)/(sin x - cos x)`


Find the derivative of f (x) = 3x at x = 2 


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


(x + 2)3


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


Differentiate of the following from first principle:

 x cos x


Differentiate  of the following from first principle:

sin (2x − 3)


tan2 


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


\[\cos \sqrt{x}\]


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


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


a0 xn + a1 xn−1 + a2 xn2 + ... + an1 x + an


\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]


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


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


x3 sin 


x2 ex log 


(x3 + x2 + 1) sin 


logx2 x


(ax + b)n (cx d)


\[\frac{x^2 + 1}{x + 1}\] 


\[\frac{e^x - \tan x}{\cot x - x^n}\] 


\[\frac{x}{1 + \tan x}\] 


\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]


\[\frac{1 + 3^x}{1 - 3^x}\]


\[\frac{\sec x - 1}{\sec x + 1}\] 


If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\] 


If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\] 


Mark the correct alternative in of the following:

Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]


Mark the correct alternative in of the following:

If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×