Advertisements
Advertisements
प्रश्न
(x2 + 1) (x − 5)
Advertisements
उत्तर
\[ \frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h \right)^3 + 4 \left( x + h \right)^2 + 3\left( x + h \right) + 2 - \left( x^3 + 4 x^2 + 3x + 2 \right)}{h}\]
\[ = \lim_{h \to 0} \frac{x^3 + 3 x^2 h + 3x h^2 + h^3 + 4 x^2 + 4 h^2 + 8xh + 3x + 3h + 2 - x^3 - 4 x^2 - 3x - 2}{h}\]
\[ = \lim_{h \to 0} \frac{3 x^2 h + 3x h^2 + h^3 + 4 h^2 + 8xh + 3h + 2}{h}\]
\[ = \lim_{h \to 0} \frac{h\left( 3 x^2 + 3xh + h^2 + 4h + 8x + 3 \right)}{h}\]
\[ = \lim_{h \to 0} \left( 3 x^2 + 3xh + h^2 + 4h + 8x + 3 \right)\]
\[ = 3 x^2 + 8x + 3\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x at x = 1.
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 + 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):
sinn 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 + a))/ cos x`
Find the derivative of f (x) x at x = 1
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
\[\frac{2}{x}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
Differentiate each of the following from first principle:
\[\sqrt{\sin (3x + 1)}\]
tan2 x
\[\tan \sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
xn tan x
(x3 + x2 + 1) sin x
sin x cos x
x2 sin x log x
sin2 x
x3 ex cos x
x5 (3 − 6x−9)
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.
\[\frac{a + \sin x}{1 + a \sin x}\]
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 derivative of f (x) = 3 |2 + x| at x = −3.
Mark the correct alternative in of the following:
Let f(x) = x − [x], x ∈ R, then \[f'\left( \frac{1}{2} \right)\]
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 \[y = \frac{1 + \frac{1}{x^2}}{1 - \frac{1}{x^2}}\] then \[\frac{dy}{dx} =\]
Find the derivative of x2 cosx.
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
