Advertisements
Advertisements
प्रश्न
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
Advertisements
उत्तर
\[\text{ Let } u = x^2 - x + 1; v = x^2 + x + 1\]
\[\text{ Then }, u' = 2x - 1; v' = 2x + 1\]
\[\text{ By quotient rule },\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x^2 - x + 1}{x^2 + x + 1} \right) = \frac{\left( x^2 + x + 1 \right)\left( 2x - 1 \right) - \left( x^2 - x + 1 \right)\left( 2x + 1 \right)}{\left( x^2 + x + 1 \right)^2}\]
\[ = \frac{2 x^3 + 2 x^2 + 2x - x^2 - x - 1 - 2 x^3 + 2 x^2 - 2x - x^2 + x - 1}{\left( x^2 + x + 1 \right)^2}\]
\[ = \frac{2 x^2 - 2}{\left( x^2 + x + 1 \right)^2}\]
\[ = \frac{2\left( x^2 - 1 \right)}{\left( x^2 + x + 1 \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (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):
`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 + 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):
`(sin(x + a))/ cos x`
Find the derivative of the following function at the indicated point:
\[\frac{1}{x^3}\]
k xn
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
sin x + cos 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 (2x + 1)
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
x3 ex
xn loga x
(x3 + x2 + 1) sin x
\[e^x \log \sqrt{x} \tan x\]
x−3 (5 + 3x)
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] 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 \[f'\left( a \right)\]
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of 2x4 + x.
`(a + b sin x)/(c + d cos x)`
