Advertisements
Advertisements
प्रश्न
(2x2 − 3) sin x
Advertisements
उत्तर
\[\text{ Let } u = 2 x^2 - 3; v = \sin x\]
\[\text{ Then }, u' = 4x; v' = \cos x\]
\[\text{ Using theproduct rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ \left( 2 x^2 - 3 \right) \sin x \right] = \left( 2 x^2 - 3 \right) \cos x + 4x \sin x \]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of 99x at x = 100.
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 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 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) = 3x at x = 2
Find the derivative of f (x) = x2 − 2 at x = 10
Find the derivative of f (x) = cos x at x = 0
\[\frac{2}{x}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{1}{x^3}\]
(x + 2)3
Differentiate of the following from first principle:
(−x)−1
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
tan2 x
\[\sin \sqrt{2x}\]
\[\cos \sqrt{x}\]
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
ex log a + ea long x + ea log a
(2x2 + 1) (3x + 2)
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
(1 +x2) cos x
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{1 + \log x}{1 - \log x}\]
\[\frac{x}{\sin^n x}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.
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 (x) = \[\log_{x_2}\]write the value of f' (x).
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
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.
