Advertisements
Advertisements
प्रश्न
(x sin x + cos x ) (ex + x2 log x)
Advertisements
उत्तर
\[\text{ Let } u = x \sin x + \cos x; v = e^x + x^2 \log x \]
\[\text{ Then }, u' = \left[ x\frac{d}{dx}\left( \sin x \right) + \sin x \frac{d}{dx}\left( x \right) \right] - \sin x \]
\[ = x \cos x + \sin x - \sin x \]
\[ = x \cos x\]
\[ v' = e^x + \left[ x^2 \frac{d}{dx}\left( \log x \right) + \log x \frac{d}{dx}\left( x^2 \right) \right]\]
\[ = e^x + x + 2x \log x \]
\[ \]
\[ \text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v ' + v u'\]
\[\frac{d}{dx}\left[ \left( x \sin x + \cos x \right)\left( e^x + x^2 \cos x \right) \right]\]
\[ = \left( x \sin x + \cos x \right)\left( e^x + x + 2x \log x \right) + \left( e^x + x^2 \log x \right) \left( x \cos x \right)\]
\[\]
APPEARS IN
संबंधित प्रश्न
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):
`(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):
`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):
(ax + b)n (cx + d)m
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 + a))/ 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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) x at x = 1
Find the derivative of f (x) = cos x at x = 0
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{3 - x}}\]
(x2 + 1) (x − 5)
Differentiate of the following from first principle:
e3x
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
x2 ex
tan (2x + 1)
(2x2 + 1) (3x + 2)
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
x2 ex log x
x2 sin x log x
sin2 x
logx2 x
\[e^x \log \sqrt{x} \tan x\]
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \sin x}{1 + \cos x}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
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\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\]
`(a + b sin x)/(c + d cos x)`
