Advertisements
Advertisements
Question
\[\frac{x + \cos x}{\tan x}\]
Advertisements
Solution
\[\text{ Let } u = x + \cos x; v = \tan x\]
\[\text{ Then }, u' = 1 - \sin x; v' = \sec^2 x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x + \cos x}{\tan x} \right) = \frac{\tan x\left( 1 - \sin x \right) - \left( x + \cos x \right) \sec^2 x}{\tan^2 x}\]
\[\]
APPEARS IN
RELATED QUESTIONS
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):
`(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):
sinn 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 3x at x = 2
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{1}{x^3}\]
Differentiate of the following from first principle:
(−x)−1
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
tan2 x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
2 sec x + 3 cot x − 4 tan x
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
(x sin x + cos x) (x cos x − sin x)
(1 − 2 tan x) (5 + 4 sin x)
(1 +x2) cos x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x−4 (3 − 4x−5)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{1}{a x^2 + bx + c}\]
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 \[\frac{d}{dx}\left( f (x) \right)\]
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
