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 (5x3 + 3x – 1) (x – 1).
Find the derivative of x5 (3 – 6x–9).
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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = tan x at x = 0
\[\frac{1}{x^3}\]
k xn
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\sqrt{\tan x}\]
3x + x3 + 33
ex log a + ea long x + ea log a
cos (x + a)
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
xn tan x
xn loga x
(x sin x + cos x) (x cos x − sin x)
(1 − 2 tan x) (5 + 4 sin x)
sin2 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.
(ax + b)n (cx + d)n
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
`(a + b sin x)/(c + d cos x)`
