Advertisements
Advertisements
प्रश्न
\[\frac{3^x}{x + \tan x}\]
Advertisements
उत्तर
\[\text{ Let } u = 3^x ; v = x + \tan x\]
\[\text{ Then }, u' = 3^x \log 3; v' = 1 + \sec^2 x\]
\[\text{ By quotient rule, we have }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{3^x}{x + \tan x} \right) = \frac{\left( x + \tan x \right) 3^x \log 3 - 3^x \left( 1 + \sec^2 x \right)}{\left( x + \tan x \right)^2}\]
\[ = \frac{3^x \left[ \left( x + \tan x \right) \log 3 - \left( 1 + \sec^2 x \right) \right]}{\left( x + \tan x \right)^2}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
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)/(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):
`cos x/(1 + sin 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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) x at x = 1
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
Differentiate of the following from first principle:
e3x
x ex
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x2 ex log x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x2 sin x log x
(1 +x2) cos x
logx2 x
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{1}{a x^2 + bx + c}\]
If \[\frac{\pi}{2}\] then find \[\frac{d}{dx}\left( \sqrt{\frac{1 + \cos 2x}{2}} \right)\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 \[\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If f (x) = \[\log_{x_2}\]write the value of f' (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
Find the derivative of 2x4 + x.
`(a + b sin x)/(c + d cos x)`
