Advertisements
Advertisements
प्रश्न
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Advertisements
उत्तर
\[\text{ Let } x = 2\]
\[\text{ We know }:\]
\[2>1 \text{ and } 2<3\]
\[\therefore x>1 \text{ and } x<3\]
\[\left| x - 1 \right| = x - 1 \text{ and } \left| x - 3 \right| = - \left( x - 3 \right) = - x + 3\]
\[f\left( x \right) = \left| x - 1 \right| + \left| x - 3 \right| = x - 1 - x + 3 = 2\]
\[f'\left( x \right) = 0\]
APPEARS IN
संबंधित प्रश्न
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):
`(1 + 1/x)/(1- 1/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):
`(px^2 +qx + r)/(ax +b)`
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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) x at x = 1
\[\frac{1}{x^3}\]
\[\frac{x + 2}{3x + 5}\]
(x2 + 1) (x − 5)
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
\[\cos \sqrt{x}\]
3x + x3 + 33
(2x2 + 1) (3x + 2)
cos (x + a)
x3 ex
(x3 + x2 + 1) sin x
(1 +x2) cos x
x3 ex cos x
x4 (5 sin x − 3 cos x)
(2x2 − 3) sin x
x5 (3 − 6x−9)
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.
(x + 2) (x + 3)
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
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 each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
(ax2 + cot x)(p + q cos x)
