Advertisements
Advertisements
प्रश्न
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Advertisements
उत्तर
\[\sqrt{\frac{1 + \cos 2x}{2}}\]
\[ = \sqrt{\frac{2 \cos^2 x}{2}}\]
\[ = \sqrt{\cos^2 x}\]
\[ = - \cos x (\because\frac{\pi}{2}<x<\pi)\]
\[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
\[ = \frac{d}{dx}\left( - \cos x \right)\]
\[ = - \left( - \sin x \right)\]
\[ = \sin x\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x2 – 2 at x = 10.
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/(ax^2 + bx + c)`
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):
sinn x
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 - 1}{x}\]
k xn
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
eax + b
Differentiate each of the following from first principle:
x2 ex
tan2 x
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
ex log a + ea long x + ea log a
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 sin x
xn tan x
xn loga x
sin x cos x
x5 ex + x6 log x
x4 (5 sin x − 3 cos x)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
(ax + b) (a + d)2
(ax + b)n (cx + d)n
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
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:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Find the derivative of f(x) = tan(ax + b), by first principle.
