Advertisements
Advertisements
प्रश्न
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
Advertisements
उत्तर
\[\frac{d}{dx}\left[ \left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right) \right]\]
\[ = \frac{d}{dx}\left[ \left( x + x^{- 1} \right)\left( x^\frac{1}{2} + x^\frac{- 1}{2} \right) \right]\]
\[ = \frac{d}{dx}\left( x^\frac{3}{2} + x^\frac{1}{2} + x^\frac{- 1}{2} + x^\frac{- 3}{2} \right)\]
\[ = \frac{d}{dx}\left( x^\frac{3}{2} \right) + \frac{d}{dx}\left( x^\frac{1}{2} \right) + \frac{d}{dx}\left( x^\frac{- 1}{2} \right) + \frac{d}{dx}\left( x^\frac{- 3}{2} \right)\]
\[ = \frac{3}{2} x^\frac{1}{2} + \frac{1}{2} x^\frac{- 1}{2} - \frac{1}{2} x^\frac{- 3}{2} - \frac{3}{2} x^\frac{- 5}{2} \]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–4 (3 – 4x–5).
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):
(ax + b)n
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 f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
k xn
(x + 2)3
(x2 + 1) (x − 5)
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
eax + b
x ex
Differentiate of the following from first principle:
(−x)−1
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
(2x2 + 1) (3x + 2)
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
x3 sin x
(x3 + x2 + 1) sin x
(1 +x2) cos x
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{3^x}{x + \tan x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
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
