Advertisements
Advertisements
प्रश्न
\[\frac{x}{1 + \tan x}\]
Advertisements
उत्तर
\[\text{ Let } u = x; v = 1 + \tan x\]
\[\text{ Then }, u' = 1; v' = \sec^2 x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x}{1 + \tan x} \right) = \frac{\left( 1 + \tan x \right)1 - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
\[ = \frac{1 + \tan x - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
`cos x/(1 + sin 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):
`(sec x - 1)/(sec x + 1)`
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
\[\frac{x^2 - 1}{x}\]
k xn
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
tan2 x
tan (2x + 1)
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
log3 x + 3 loge x + 2 tan x
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
sin x cos x
(x sin x + cos x ) (ex + x2 log x)
x3 ex cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x4 (5 sin x − 3 cos x)
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{\sin^n x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
