Advertisements
Advertisements
प्रश्न
\[\frac{ax + b}{p x^2 + qx + r}\]
Advertisements
उत्तर
\[\text{ Let } u = ax + b; v = p x^2 + qx + r\]
\[\text{ Then }, u' = a; v' = 2px + q\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{ax + b}{p x^2 + qx + r} \right) = \frac{\left( p x^2 + qx + r \right)a - \left( ax + b \right)\left( 2px + q \right)}{\left( p x^2 + qx + r \right)^2}\]
\[ = \frac{ap x^2 + aq x + ar - 2ap x^2 - 2bp x - aq x - bq}{\left( p x^2 + qx + r \right)^2}\]
\[ = \frac{- ap x^2 - 2bp x + ar - bq}{\left( p x^2 + qx + r \right)^2}\]
APPEARS IN
संबंधित प्रश्न
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) (cx + d)2
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):
`a/x^4 = b/x^2 + 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):
`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):
`(sec x - 1)/(sec x + 1)`
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 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = cos x at x = 0
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 sin x
\[\sqrt{\tan x}\]
3x + x3 + 33
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
log3 x + 3 loge x + 2 tan x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
cos (x + a)
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
(x3 + x2 + 1) sin x
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
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 x2 cosx.
(ax2 + cot x)(p + q cos x)
`(a + b sin x)/(c + d cos x)`
