Advertisements
Advertisements
प्रश्न
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Advertisements
उत्तर
\[\text{ Case } 1:\]
\[x > 0\]
\[|x| = x\]
\[\text{ Thus, we have }:\]
\[\frac{d}{dx}\left( x|x| \right) = \frac{d}{dx}\left( x . x \right) = \frac{d}{dx}\left( x^2 \right) = 2x \left( 1 \right)\]
\[\text{ Case } 2:\]
\[x < 0\]
\[|x| = - x\]
\[\text{ Thus, we have }:\]
\[\frac{d}{dx}\left( x|x| \right) = \frac{d}{dx}\left( x . \left( - x \right) \right) = \frac{d}{dx}\left( - x^2 \right) = - 2x \left( 2 \right)\]
\[\text{ From } (1) \text{ and } (2), \text{ we have }:\]
\[\frac{d}{dx}\left( x|x| \right) = \binom{2x, if x > 0}{ - 2x, if x < 0}\]
\[\]
APPEARS IN
संबंधित प्रश्न
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):
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):
`cos x/(1 + sin 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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = 99x at x = 100
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan2 x
\[\cos \sqrt{x}\]
x4 − 2 sin x + 3 cos x
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 sin x
x2 ex log x
xn loga x
logx2 x
x3 ex cos x
(2x2 − 3) sin 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)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Find the derivative of 2x4 + x.
Find the derivative of f(x) = tan(ax + b), by first principle.
(ax2 + cot x)(p + q cos x)
