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
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 `2x - 3/4`
Find the derivative of (5x3 + 3x – 1) (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):
`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):
`(sin x + cos x)/(sin x - 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):
sinn x
Find the derivative of f (x) x at x = 1
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan (2x + 1)
(2x2 + 1) (3x + 2)
log3 x + 3 loge x + 2 tan x
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 ex
\[\frac{2^x \cot x}{\sqrt{x}}\]
x2 sin x log x
(1 +x2) cos x
x3 ex cos x
x−4 (3 − 4x−5)
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
