Advertisements
Advertisements
प्रश्न
log3 x + 3 loge x + 2 tan x
Advertisements
उत्तर
\[\frac{d}{dx}\left( \log_3 x + 3 \log_e x + 2 \tan x \right)\]
\[ = \frac{d}{dx}\left( \frac{\log x}{\log 3} \right) + 3\frac{d}{dx}\left( \log_e x \right) + 2\frac{d}{dx}\left( \tan x \right)\]
\[ = \frac{1}{\log 3} . \frac{1}{x} + 3 . \frac{1}{x} + 2 \sec^2 x\]
\[ = \frac{1}{x \log 3} + \frac{3}{x} + 2 \sec^2 x\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
Find the derivative of x at x = 1.
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^2 +qx + r)/(ax +b)`
Find the derivative of f (x) = x2 − 2 at x = 10
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
tan2 x
tan (2x + 1)
\[\tan \sqrt{x}\]
\[\frac{2 x^2 + 3x + 4}{x}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
x3 sin x
(x3 + x2 + 1) sin x
(x sin x + cos x) (x cos x − sin x)
(x sin x + cos x ) (ex + x2 log x)
\[e^x \log \sqrt{x} \tan x\]
(2x2 − 3) sin x
x5 (3 − 6x−9)
(ax + b)n (cx + d)n
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{x + \cos x}{\tan x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
Mark the correct alternative in of the following:
If \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
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
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of 2x4 + x.
Find the derivative of f(x) = tan(ax + b), by first principle.
