Advertisements
Advertisements
प्रश्न
ex log a + ea long x + ea log a
Advertisements
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
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
`(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):
`4sqrtx - 2`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of the following function at the indicated point:
sin 2x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{x^3}\]
\[\frac{x + 2}{3x + 5}\]
Differentiate each of the following from first principle:
e−x
x ex
Differentiate of the following from first principle:
x sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 ex
(2x2 + 1) (3x + 2)
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
(x3 + x2 + 1) sin x
x2 sin x log x
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x \sin x}{1 + \cos x}\]
Write the value of \[\lim_{x \to c} \frac{f(x) - f(c)}{x - c}\]
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 \[\frac{d}{dx}\left( f (x) \right)\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
`(a + b sin x)/(c + d cos x)`
