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 x–4 (3 – 4x–5).
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)2
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):
(ax + b)n
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 f (x) = 3x at x = 2
\[\frac{2}{x}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
x2 + x + 3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan (2x + 1)
\[\sqrt{\tan x}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
sin x cos x
sin2 x
x−4 (3 − 4x−5)
x−3 (5 + 3x)
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{1 + \tan x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
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\[f\left( x \right) = 1 + x + \frac{x^2}{2} + . . . + \frac{x^{100}}{100}\] then \[f'\left( 1 \right)\] is equal to
`(a + b sin x)/(c + d cos x)`
