Advertisements
Advertisements
प्रश्न
(2x2 + 1) (3x + 2)
Advertisements
उत्तर
\[\frac{d}{dx}\left( \left( 2 x^2 + 1 \right)\left( 3x + 2 \right) \right)\]
\[ = \frac{d}{dx}\left( 6 x^3 + 4 x^2 + 3x + 2 \right)\]
\[ = 6\frac{d}{dx}\left( x^3 \right) + 4\frac{d}{dx}\left( x^2 \right) + 3\frac{d}{dx}\left( x \right) + \frac{d}{dx}\left( 2 \right)\]
\[ = 6\left( 3 x^2 \right) + 4\left( 2x \right) + 3\left( 1 \right) + 0\]
\[ = 18 x^2 + 8x + 3\]
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)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):
cosec x cot 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):
`(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):
x4 (5 sin x – 3 cos x)
Find the derivative of the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{1}{\sqrt{x}}\]
\[\frac{x^2 + 1}{x}\]
x2 + x + 3
(x + 2)3
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
tan 2x
\[\tan \sqrt{x}\]
x4 − 2 sin x + 3 cos x
3x + x3 + 33
2 sec x + 3 cot x − 4 tan x
\[\frac{(x + 5)(2 x^2 - 1)}{x}\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
x5 ex + x6 log x
(x sin x + cos x ) (ex + x2 log x)
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same.
(ax + b)n (cx + d)n
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{2x - 1}{x^2 + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x \tan x}{\sec x + \tan x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
\[\frac{x^5 - \cos x}{\sin x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
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 f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
(ax2 + cot x)(p + q cos x)
