Advertisements
Advertisements
प्रश्न
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
विकल्प
\[\frac{5}{4}\]
\[\frac{4}{5}\]
1
0
Advertisements
उत्तर
\[ = \frac{1}{2}\sqrt{x} - \frac{2}{\sqrt{x}}\]
\[ = \frac{1}{2} x^\frac{1}{2} - 2 x^{- \frac{1}{2}}\]
Differentiating both sides with respect to x, we get
\[f'\left( x \right) = \frac{1}{2} \times \frac{1}{2} x^\frac{1}{2} - 1 - 2 \times \left( - \frac{1}{2} \right) x^{- \frac{1}{2} - 1} \left[ f\left( x \right) = x^n \Rightarrow f'\left( x \right) = n x^{n - 1} \right]\]
\[ \Rightarrow f'\left( x \right) = \frac{1}{4} x^{- \frac{1}{2}} + x^{- \frac{3}{2}} \]
\[ \therefore f'\left( 1 \right) = \frac{1}{4} \times 1 + 1 = \frac{5}{4}\]
Hence, the correct answer is option (a).
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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):
(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):
(ax + b)n (cx + d)m
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 + bsin x)/(c + dcosx)`
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) x at x = 1
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 2}{3x + 5}\]
x2 + x + 3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
\[\tan \sqrt{x}\]
3x + x3 + 33
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
\[e^x \log \sqrt{x} \tan x\]
x3 ex cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of 2x4 + x.
