Advertisements
Advertisements
प्रश्न
x2 ex log x
Advertisements
उत्तर
\[\text{ Let } u = x^2 ; v = e^x ; w = \log x\]
\[\text{ Then }, u' = 2x; v' = e^x , w = \frac{1}{x}\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uvw \right) = u'vw + + uv'w + uvw'\]
\[\frac{d}{dx}\left( x^2 e^x \log x \right) = 2x e^x \log x + x^2 e^x \log x + x^2 e^x \frac{1}{x}\]
\[ = 2x e^x \log x + x^2 e^x \log x + x e^x \]
\[ = x e^x \left( 2 \log x + x \log x + 1 \right)\]
APPEARS IN
संबंधित प्रश्न
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):
(x + a)
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 f (x) = 3x at x = 2
Find the derivative of f (x) x at x = 1
\[\frac{x^2 + 1}{x}\]
(x + 2)3
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
eax + b
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
sin (x + 1)
Differentiate each of the following from first principle:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[e^\sqrt{ax + b}\]
Differentiate each of the following from first principle:
\[3^{x^2}\]
\[\sin \sqrt{2x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
xn loga x
(1 − 2 tan x) (5 + 4 sin x)
\[e^x \log \sqrt{x} \tan x\]
x3 ex cos x
(2x2 − 3) sin x
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{2^x \cot x}{\sqrt{x}}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{1 + \tan x}\]
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.
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\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
