Advertisements
Advertisements
प्रश्न
\[\frac{\sec x - 1}{\sec x + 1}\]
Advertisements
उत्तर
\[\text{ Then }, u' = \sec x tan x; v' = \sec x \tan x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{sec x - 1}{sec x + 1} \right) = \frac{\left( \sec x + 1 \right)\sec x \tan x - \left( \sec x - 1 \right)\sec x \tan x}{\left( sec x + 1 \right)^2}\]
\[ = \frac{\sec^2 x \tan x + \sec x \tan x - \sec^2 x \tan x + \sec x \tan x}{\left( \sec x + 1 \right)^2}\]
\[ = \frac{2\sec x \tan x}{\left( \sec x + 1 \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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)/(cx + d)`
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/x^4 = b/x^2 + 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):
`4sqrtx - 2`
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):
cosec x cot x
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{x + 2}{3x + 5}\]
x2 + x + 3
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\sin \sqrt{2x}\]
\[\tan \sqrt{x}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x5 ex + x6 log x
\[e^x \log \sqrt{x} \tan x\]
x3 ex cos x
x4 (5 sin x − 3 cos x)
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x + \cos x}{\tan x}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
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
(ax2 + cot x)(p + q cos x)
