Advertisements
Advertisements
प्रश्न
\[\frac{e^x + \sin x}{1 + \log x}\]
Advertisements
उत्तर
\[\text{ Let } u = e^x + \sin x; v = 1 + \log x\]
\[\text{ Then }, u' = e^x + \cos x; v' = \frac{1}{x}\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{e^x + \sin x}{1 + \log x} \right) = \frac{\left( 1 + \log x \right)\left( e^x + \cos x \right) - \left( e^x + \sin x \right)\left( \frac{1}{x} \right)}{\left( 1 + \log x \right)^2}\]
\[ = \frac{x\left( 1 + \log x \right)\left( e^x + \cos x \right) - \left( e^x + \sin x \right)}{x \left( 1 + \log x \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of `2x - 3/4`
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):
`(px+ q) (r/s + s)`
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):
`(px^2 +qx + r)/(ax +b)`
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 (cx + d)m
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):
`cos x/(1 + sin x)`
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{x^3}\]
\[\frac{x + 2}{3x + 5}\]
k xn
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
sin x + cos x
\[\sin \sqrt{2x}\]
ex log a + ea long x + ea log a
log3 x + 3 loge x + 2 tan x
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
x5 ex + x6 log x
(x sin x + cos x) (x cos x − sin x)
(1 +x2) cos x
(2x2 − 3) sin x
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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 \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 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 2x4 + x.
`(a + b sin x)/(c + d cos x)`
