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 x2 – 2 at x = 10.
Find the derivative of 99x at x = 100.
Find the derivative of `2x - 3/4`
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/(ax^2 + bx + c)`
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):
`(px^2 +qx + r)/(ax +b)`
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)
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):
`(sec x - 1)/(sec x + 1)`
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 the following function at the indicated point:
2 cos x at x =\[\frac{\pi}{2}\]
\[\frac{x^2 - 1}{x}\]
\[\frac{x + 1}{x + 2}\]
\[\frac{x + 2}{3x + 5}\]
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
x2 sin x
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
Differentiate each of the following from first principle:
x2 ex
3x + x3 + 33
log3 x + 3 loge x + 2 tan x
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 sin x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(x sin x + cos x ) (ex + x2 log x)
(1 − 2 tan x) (5 + 4 sin x)
logx2 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.
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{{10}^x}{\sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{p x^2 + qx + r}{ax + b}\]
Write the value of \[\frac{d}{dx}\left( x \left| x \right| \right)\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
If |x| < 1 and y = 1 + x + x2 + x3 + ..., then write the value of \[\frac{dy}{dx}\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
