Advertisements
Advertisements
प्रश्न
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Advertisements
उत्तर
\[\text{ Case } 1: x>0\]
\[\left| x \right| = x\]
\[f\left( x \right) = \frac{x^2}{\left| x \right|} = \frac{x^2}{x} = x\]
\[f'\left( x \right) = 1\]
\[\text{ Case } 2: x<0\]
\[\left| x \right| = - x\]
\[f\left( x \right) = \frac{x^2}{\left| x \right|} = \frac{x^2}{- x} = - x\]
\[f'\left( x \right) = - 1\]
\[\text{ From case 1 and case 2, we have }:\]
`f'(x)={(1, if, x > 0),(-1, 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)`
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 f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{x + 1}{x + 2}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
eax + b
x ex
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:
\[e^\sqrt{2x}\]
ex log a + ea long x + ea log a
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
xn loga x
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
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 value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 \[\frac{dy}{dx}\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
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
(ax2 + cot x)(p + q cos x)
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
