English

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

Advertisements
Advertisements

Question

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

Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 30: Derivatives - Exercise 30.1 [Page 3]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 30 Derivatives
Exercise 30.1 | Q 7.2 | Page 3

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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):

`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):

`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 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):

sinn 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) = 99x at x = 100 


Find the derivative of f (x) = cos x at x = 0


(x + 2)3


Differentiate  of the following from first principle:

e3x


Differentiate  of the following from first principle:

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


Differentiate each of the following from first principle:

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


Differentiate each of the following from first principle: 

sin x + cos x


tan (2x + 1) 


 tan 2x 


\[\tan \sqrt{x}\]


\[\tan \sqrt{x}\] 


x4 − 2 sin x + 3 cos x


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


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

 

x3 sin x 


xn loga x 


(x sin x + cos x) (x cos x − sin x) 


(1 − 2 tan x) (5 + 4 sin x)


\[e^x \log \sqrt{x} \tan x\] 


\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\] 


x4 (5 sin x − 3 cos x)


(ax + b)n (cx + d)n 


\[\frac{x^2 + 1}{x + 1}\] 


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


\[\frac{3^x}{x + \tan x}\] 


Mark the correct alternative in of the following:

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


Find the derivative of f(x) = tan(ax + b), by first principle.


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


Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×