Advertisements
Advertisements
प्रश्न
x2 + x + 3
उत्तर
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\left( x + h \right)^2 + x + h + 3 - \left( x^2 + x + 3 \right)}{h}\]
\[ = \lim_{h \to 0} \frac{x^2 + h^2 + 2xh + x + h + 3 - x^2 - x - 3}{h}\]
\[ = \lim_{h \to 0} \frac{h^2 + 2xh + h}{h}\]
\[ = \lim_{h \to 0} \frac{h(h + 2x + 1)}{h}\]
\[ = \lim_{h \to 0} h + 2x + 1\]
\[ = 0 + 2x + 1\]
\[ = 2x + 1\]
APPEARS IN
संबंधित प्रश्न
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
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):
`cos x/(1 + sin x)`
Find the derivative of f (x) = 3x at x = 2
\[\frac{x + 2}{3x + 5}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
e3x
Differentiate of the following from first principle:
− x
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:
x2 sin x
Differentiate each of the following from first principle:
x2 ex
Differentiate each of the following from first principle:
\[3^{x^2}\]
tan 2x
\[\cos \sqrt{x}\]
3x + x3 + 33
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
x3 ex
xn loga x
(x3 + x2 + 1) sin x
(ax + b) (a + d)2
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
If x < 2, then write the value of \[\frac{d}{dx}(\sqrt{x^2 - 4x + 4)}\]
If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\]
Mark the correct alternative in of the following:
If \[y = \sqrt{x} + \frac{1}{\sqrt{x}}\] then \[\frac{dy}{dx}\] at x = 1 is
Mark the correct alternative in of the following:
If \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
Find the derivative of x2 cosx.
Find the derivative of f(x) = tan(ax + b), by first principle.
