Advertisements
Advertisements
Question
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Advertisements
Solution
\[\text{ Let } x = 2\]
\[\text{ We know }:\]
\[2>1 \text{ and } 2<3\]
\[\therefore x>1 \text{ and } x<3\]
\[\left| x - 1 \right| = x - 1 \text{ and } \left| x - 3 \right| = - \left( x - 3 \right) = - x + 3\]
\[f\left( x \right) = \left| x - 1 \right| + \left| x - 3 \right| = x - 1 - x + 3 = 2\]
\[f'\left( x \right) = 0\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x5 (3 – 6x–9).
Find the derivative of x–4 (3 – 4x–5).
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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = tan x at x = 0
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
eax + b
x ex
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
sin (2x − 3)
tan2 x
3x + x3 + 33
ex log a + ea long x + ea log a
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
xn tan x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(x sin x + cos x ) (ex + x2 log x)
logx2 x
(2x2 − 3) sin x
x−4 (3 − 4x−5)
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)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of 2x4 + x.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
