Advertisements
Advertisements
Question
\[\frac{x}{1 + \tan x}\]
Advertisements
Solution
\[\text{ Let } u = x; v = 1 + \tan x\]
\[\text{ Then }, u' = 1; v' = \sec^2 x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x}{1 + \tan x} \right) = \frac{\left( 1 + \tan x \right)1 - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
\[ = \frac{1 + \tan x - x \sec^2 x}{\left( 1 + \tan x \right)^2}\]
\[\]
APPEARS IN
RELATED QUESTIONS
Find the derivative of x5 (3 – 6x–9).
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{x^2 + 1}{x}\]
\[\frac{1}{\sqrt{3 - x}}\]
x2 + x + 3
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan2 x
tan 2x
x4 − 2 sin x + 3 cos x
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
xn loga x
x4 (5 sin x − 3 cos x)
x−3 (5 + 3x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
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 f(x) = tan(ax + b), by first principle.
