Advertisements
Advertisements
प्रश्न
\[\frac{1}{a x^2 + bx + c}\]
Advertisements
उत्तर
\[\text{ Let } u = 1; v = a x^2 + bx + c\]
\[\text{ Then }, u' = 0; v' = 2ax + b\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{1}{a x^2 + bx + c} \right) = \frac{\left( a x^2 + bx + c \right)0 - 1\left( 2ax + b \right)}{\left( a x^2 + bx + c \right)^2}\]
\[ = \frac{- \left( 2ax + b \right)}{\left( a x^2 + bx + c \right)^2}\]
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
Find the derivative of x–3 (5 + 3x).
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):
`(a + bsin x)/(c + dcosx)`
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 + a))/ cos x`
Find the derivative of f (x) = cos x at x = 0
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{x^3}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
x2 ex log x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x5 ex + x6 log x
x−4 (3 − 4x−5)
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
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
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of 2x4 + x.
Find the derivative of x2 cosx.
`(a + b sin x)/(c + d cos x)`
