Advertisements
Advertisements
प्रश्न
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Advertisements
उत्तर
\[\text{ Given }: x<2\]
\[\therefore 2-x>0\]
\[\frac{d}{dx}\left( \sqrt{x^2 - 4x + 4} \right)\]
\[ = \frac{d}{dx}\left( \sqrt{\left( 2 - x \right)^2} \right)\]
\[ = \frac{d}{dx}\left( 2 - x \right) (\because 2-x>0)\]
\[ = 0 - 1\]
\[ = - 1\]
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):
(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):
`(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):
`(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):
`(sin(x + a))/ cos x`
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x + 1}{x + 2}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
sin x + cos x
tan (2x + 1)
\[\tan \sqrt{x}\]
\[\frac{2 x^2 + 3x + 4}{x}\]
sin2 x
x5 (3 − 6x−9)
\[\frac{e^x}{1 + x^2}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
If f (x) = \[\log_{x_2}\]write the value of f' (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 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.
`(a + b sin x)/(c + d cos x)`
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
