Advertisements
Advertisements
प्रश्न
\[\frac{x + \cos x}{\tan x}\]
Advertisements
उत्तर
\[\text{ Let } u = x + \cos x; v = \tan x\]
\[\text{ Then }, u' = 1 - \sin x; v' = \sec^2 x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{x + \cos x}{\tan x} \right) = \frac{\tan x\left( 1 - \sin x \right) - \left( x + \cos x \right) \sec^2 x}{\tan^2 x}\]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of (5x3 + 3x – 1) (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):
`(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):
`(sin x + cos x)/(sin x - cos x)`
Find the derivative of f (x) x at x = 1
\[\frac{2}{x}\]
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
− x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan (2x + 1)
x4 − 2 sin x + 3 cos x
ex log a + ea long x + ea log a
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
cos (x + a)
x3 sin x
x2 ex log x
logx2 x
\[e^x \log \sqrt{x} \tan x\]
x5 (3 − 6x−9)
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
(ax + b)n (cx + d)n
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
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 f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of x2 cosx.
