Advertisements
Advertisements
प्रश्न
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Advertisements
उत्तर
\[\text{ Case } 1: x>0\]
\[\left| x \right| = x . . . \left( 1 \right)\]
\[\frac{d}{dx}\left( \log \left| x \right| \right) = \log x\]
\[ = \frac{1}{x}\]
\[ = \frac{1}{\left| x \right|} (\text{ from } (1))\]
\[Case 2:x<0\]
\[\left| x \right| = - x . . . \left( 2 \right)\]
\[\frac{d}{dx}\left( \log \left| x \right| \right) = \log \left( - x \right)\]
\[ = \frac{1}{- x}\]
\[ = \frac{1}{\left| x \right|} (\text{ from } (2))\]
\[\text{ From case } (1) \text{ and case }(2),\]
\[\frac{d}{dx}\left( \log \left| x \right| \right) = \frac{1}{\left| x \right|}\]
APPEARS IN
संबंधित प्रश्न
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):
(ax + b) (cx + d)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):
`4sqrtx - 2`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) x at x = 1
\[\frac{1}{x^3}\]
x2 + x + 3
(x + 2)3
(x2 + 1) (x − 5)
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x cos x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
x2 ex
\[\tan \sqrt{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 ex
x2 ex log x
x2 sin x log x
x5 ex + x6 log x
(1 − 2 tan x) (5 + 4 sin x)
logx2 x
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)
\[\frac{e^x}{1 + x^2}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Find the derivative of 2x4 + x.
