Advertisements
Advertisements
प्रश्न
\[\frac{1}{a x^2 + bx + c}\]
Advertisements
उत्तर
\[\frac{d}{dx}\left( \frac{1}{a x^2 + bx + c} \right)\]
\[ = \frac{d}{dx} \left( a x^2 + bx + c \right)^{- 1} \]
\[ = \left( - 1 \right) \left( a x^2 + bx + c \right)^{- 2} \frac{d}{dx}\left( a x^2 + bx + c \right) (\text{ Using the chain rule })\]
\[ = \left( - 1 \right) \left( a x^2 + bx + c \right)^{- 2} \left( 2ax + b \right)\]
\[ = \frac{- \left( 2ax + b \right)}{\left( a x^2 + bx + c \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
Find the derivative of 99x at x = 100.
Find the derivative of x at x = 1.
Find the derivative of `2/(x + 1) - x^2/(3x -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):
`(ax + b)/(cx + d)`
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):
sinn x
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = 99x at x = 100
x2 + x + 3
(x2 + 1) (x − 5)
Differentiate each of the following from first principle:
e−x
x ex
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
\[\tan \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
2 sec x + 3 cot x − 4 tan x
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
x3 ex
(1 +x2) cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
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.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
(ax + b)n (cx + d)n
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{1 + \tan x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Find the derivative of 2x4 + x.
`(a + b sin x)/(c + d cos x)`
