Advertisements
Advertisements
प्रश्न
x5 ex + x6 log x
Advertisements
उत्तर
\[ = x^5 \frac{d}{dx}\left( e^x \right) + e^x \frac{d}{dx}\left( x^5 \right) + x^6 \frac{d}{dx}\left( \log x \right) + \log x \frac{d}{dx}\left( x^6 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^6 . \frac{1}{x} + \log x\left( 6 x^5 \right)\]
\[ = x^5 e^x + e^x \left( 5 x^4 \right) + x^5 + \log x\left( 6 x^5 \right)\]
\[ = x^4 \left( x e^x + 5 e^x + x + 6x \log x \right)\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
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)`
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 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):
`(a + bsin x)/(c + dcosx)`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
x2 + x + 3
(x2 + 1) (x − 5)
\[\sqrt{2 x^2 + 1}\]
x ex
Differentiate of the following from first principle:
x cos x
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
\[\sin \sqrt{2x}\]
3x + x3 + 33
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
x2 ex log x
(ax + b) (a + d)2
(ax + b)n (cx + d)n
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}\]
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 \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
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
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
`(a + b sin x)/(c + d cos x)`
