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
Find the derivative of x5 (3 – 6x–9).
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)`
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):
`(1 + 1/x)/(1- 1/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):
(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):
`(sin x + cos x)/(sin x - cos 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):
sinn x
Find the derivative of f (x) = x2 − 2 at x = 10
\[\frac{x + 1}{x + 2}\]
\[\sqrt{2 x^2 + 1}\]
\[\frac{2x + 3}{x - 2}\]
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
x2 sin x
\[\sqrt{\tan x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
\[\frac{2^x \cot x}{\sqrt{x}}\]
logx2 x
x4 (5 sin x − 3 cos x)
x5 (3 − 6x−9)
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{1}{a x^2 + bx + c}\]
If f (x) = |x| + |x−1|, write the value of \[\frac{d}{dx}\left( f (x) \right)\]
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 \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
`(a + b sin x)/(c + d cos x)`
