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.
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):
sin (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):
`(a + bsin x)/(c + dcosx)`
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 =\[\frac{\pi}{2}\]
k xn
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
\[\cos \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
xn loga x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x−4 (3 − 4x−5)
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{\sec x - 1}{\sec x + 1}\]
\[\frac{x + \cos x}{\tan x}\]
\[\frac{x}{\sin^n x}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
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 \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
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
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
