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 99x at x = 100.
Find the derivative of (5x3 + 3x – 1) (x – 1).
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):
`(px^2 +qx + r)/(ax +b)`
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 f (x) = x2 − 2 at x = 10
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
k xn
x2 + x + 3
Differentiate of the following from first principle:
e3x
x ex
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 sin x
\[\sin \sqrt{2x}\]
\[\tan \sqrt{x}\]
\[\tan \sqrt{x}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
2 sec x + 3 cot x − 4 tan x
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x3 sin x
(x3 + x2 + 1) sin x
sin x cos x
x4 (5 sin x − 3 cos x)
x−4 (3 − 4x−5)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Find the derivative of 2x4 + x.
(ax2 + cot x)(p + q cos x)
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
