Advertisements
Advertisements
Question
\[\frac{ax + b}{p x^2 + qx + r}\]
Advertisements
Solution
\[\text{ Let } u = ax + b; v = p x^2 + qx + r\]
\[\text{ Then }, u' = a; v' = 2px + q\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{ax + b}{p x^2 + qx + r} \right) = \frac{\left( p x^2 + qx + r \right)a - \left( ax + b \right)\left( 2px + q \right)}{\left( p x^2 + qx + r \right)^2}\]
\[ = \frac{ap x^2 + aq x + ar - 2ap x^2 - 2bp x - aq x - bq}{\left( p x^2 + qx + r \right)^2}\]
\[ = \frac{- ap x^2 - 2bp x + ar - bq}{\left( p x^2 + qx + r \right)^2}\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x at x = 1.
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 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):
(x + a)
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)/(px^2 + qx + r)`
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):
`(sec x - 1)/(sec x + 1)`
x2 + x + 3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 sin x
x3 ex
sin x cos x
(x sin x + cos x) (x cos x − sin x)
(x sin x + cos x ) (ex + x2 log x)
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
(ax2 + cot x)(p + q cos x)
