Advertisements
Advertisements
Question
x−3 (5 + 3x)
Advertisements
Solution
\[\text{ Let } u = x^{- 3} ; v = \left( 5 + 3x \right)\]
\[\text{ Then }, u = - 3 x^{- 4} ; v' = 3\]
\[\text{ Using the product rule } :\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ x^3 \left( 5 + 3x \right) \right] = x^{- 3} . 3 + \left( 5 + 3x \right) \left( - 3 x^{- 4} \right)\]
\[ = 3 x^{- 3} - 15 x^{- 4} - 9 x^{- 3} \]
\[ = - 15 x^{- 4} - 6 x^{- 3}\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x2 – 2 at x = 10.
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
Find the derivative of f (x) x at x = 1
\[\frac{x + 2}{3x + 5}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
eax + b
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\sqrt{\tan x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
cos (x + a)
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
(1 − 2 tan x) (5 + 4 sin x)
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)
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)
(ax + b) (a + d)2
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
