Advertisements
Advertisements
प्रश्न
Write the derivative of f (x) = 3 |2 + x| at x = −3.
Advertisements
उत्तर
\[\text{ Let } x = -3\]
\[\text{ We know }:\]
\[-3<-2\]
\[\text{ Thus, we have }:\]
\[x<-2\]
\[\text{ It gives } x+2<0.\]
\[ \therefore \left| 2 + x \right| = \left| x + 2 \right| = - \left( x + 2 \right) = - x - 2\]
\[f\left( x \right) = 3 \left| 2 + x \right| = 3\left( - x - 2 \right) = - 3x - 6\]
\[f'\left( x \right) = - 3\frac{d}{dx}\left( x \right) - \frac{d}{dx}\left( 6 \right) = - 3\]
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):
`1/(ax^2 + bx + c)`
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)n (cx + d)m
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):
`(sin x + cos x)/(sin x - cos 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) = tan x at x = 0
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 + 1}{x}\]
x2 + x + 3
(x + 2)3
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
\[\tan \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
cos (x + a)
sin x cos x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x3 ex cos x
x5 (3 − 6x−9)
x−4 (3 − 4x−5)
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)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x + \cos x}{\tan x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Find the derivative of f(x) = tan(ax + b), by first principle.
