Advertisements
Advertisements
प्रश्न
ex log a + ea long x + ea log a
उत्तर
\[\frac{d}{dx}\left( e^{x \log a} + e^{a \log x} + e^{a \log a} \right)\]
\[ = \frac{d}{dx}\left( e^{x \log a} \right) + \frac{d}{dx}\left( e^{a \log x} \right) + \frac{d}{dx}\left( e^{a \log a} \right)\]
`= \frac{d}{dx}\left( e^\log a^x \right) + \frac{d}{dx}\left( {e^\log x}^a \right) + \frac{d}{dx}\left( e^\log a^a \right)`
`= \frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^a \right) + \frac{d}{dx}\left( a^a \right)`
\[ = a^x \log a + a x^{a - 1} + 0 \]
\[ = a^x \log a + a x^{a - 1}\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
Find the derivative of (5x3 + 3x – 1) (x – 1).
Find the derivative of x5 (3 – 6x–9).
Find the derivative of f (x) = 3x at x = 2
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{x^3}\]
\[\frac{x + 2}{3x + 5}\]
x2 + x + 3
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
tan 2x
\[\cos \sqrt{x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
log3 x + 3 loge x + 2 tan x
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{2 x^2 + 3x + 4}{x}\]
2 sec x + 3 cot x − 4 tan x
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
(x3 + x2 + 1) sin x
logx2 x
x−4 (3 − 4x−5)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)
(ax + b)n (cx + d)n
\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{x + \cos x}{\tan x}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
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 \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of x2 cosx.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
