Advertisements
Advertisements
प्रश्न
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
उत्तर
\[\frac{d}{dx}\left( \frac{a \cos x + b \sin x + c}{\sin x} \right)\]
\[ = \frac{d}{dx}\left( \frac{a \cos x}{\sin x} \right) + \frac{d}{dx}\left( \frac{b \sin x}{\sin x} \right) + \frac{d}{dx}\left( \frac{c}{\sin x} \right)\]
\[ = a\frac{d}{dx}\left( cot x \right) + \frac{d}{dx}\left( b \right) + c\frac{d}{dx}\left( \cos ec x \right)\]
\[ = - a \cos e c^2 x + 0 - c \cos ec x cot x\]
\[ = - a \cos e c^2 x - c \cos ec x cot x\]
APPEARS IN
संबंधित प्रश्न
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)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):
`(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):
`4sqrtx - 2`
Find the derivative of f (x) = 3x at x = 2
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) = cos x at x = 0
\[\frac{x + 1}{x + 2}\]
(x + 2)3
\[\sqrt{2 x^2 + 1}\]
Differentiate of the following from first principle:
− x
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:
x2 ex
\[\sin \sqrt{2x}\]
(2x2 + 1) (3x + 2)
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]
x3 ex
(x3 + x2 + 1) sin x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(1 − 2 tan x) (5 + 4 sin x)
x−4 (3 − 4x−5)
x−3 (5 + 3x)
\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{3^x}{x + \tan x}\]
\[\frac{x}{\sin^n x}\]
\[\frac{1}{a x^2 + bx + c}\]
Write the derivative of f (x) = 3 |2 + x| at x = −3.
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 \[y = \frac{\sin\left( x + 9 \right)}{\cos x}\] then \[\frac{dy}{dx}\] at x = 0 is
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 f(x) = tan(ax + b), by first principle.
