Advertisements
Advertisements
प्रश्न
\[\frac{x}{1 + \tan x}\]
Advertisements
उत्तर
\[\text{ Let } u = x; v = 1 + \tan x\]
\[\text{ Then }, u' = 1; v' = \sec^2 x\]
\[\text{ Using thequotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[ = \frac{\left( 1 + \tan x \right) \times 1 - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
\[ = \frac{1 + \tan x - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
Find the derivative of x–4 (3 – 4x–5).
Find the derivative of `2/(x + 1) - x^2/(3x -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):
(ax + b) (cx + d)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):
`(1 + 1/x)/(1- 1/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):
`(ax + b)/(px^2 + qx + r)`
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):
(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):
x4 (5 sin x – 3 cos 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 =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
x ex
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan2 x
3x + x3 + 33
\[\frac{2 x^2 + 3x + 4}{x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
xn loga x
(1 − 2 tan x) (5 + 4 sin x)
(1 +x2) cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of 2x4 + x.
