Advertisements
Advertisements
प्रश्न
\[\frac{a + b \sin x}{c + d \cos x}\]
Advertisements
उत्तर
\[\text{ Let } u = a + b \sin x; v = c + d \cos x\]
\[\text{ Then }, u' = b \cos x; v' = - d \sin x\]
\[\text{ Using the quotient rule }:\]
\[\frac{d}{dx}\left( \frac{u}{v} \right) = \frac{vu' - uv'}{v^2}\]
\[\frac{d}{dx}\left( \frac{a + b \sin x}{c + d \cos x} \right) = \frac{\left( c + d \cos x \right)b \cos x - \left( a + b \sin x \right)\left( - d \sin x \right)}{\left( c + d \cos x \right)^2}\]
\[ = \frac{bc \cos x + bd \cos^2 x + ad \sin x + bd \sin^2 x}{\left( c + d \cos x \right)^2}\]
\[ = \frac{bc \cos x + ad \sin x + bd \left( \sin^2 x + \cos^2 x \right)}{\left( c + d \cos x \right)^2}\]
\[ = \frac{bc \cos x + ad \sin x + bd}{\left( c + d \cos x \right)^2}\]
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):
`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):
`a/x^4 = b/x^2 + 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):
(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):
x4 (5 sin x – 3 cos x)
Find the derivative of f (x) = cos x at x = 0
\[\sqrt{2 x^2 + 1}\]
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
e3x
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:
\[\frac{\sin x}{x}\]
Differentiate each of the following from first principle:
\[e^{x^2 + 1}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\sqrt{\tan x}\]
\[\tan \sqrt{x}\]
(2x2 + 1) (3x + 2)
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]
\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
sin x cos x
sin2 x
x4 (5 sin x − 3 cos x)
x−3 (5 + 3x)
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x + \cos x}{\tan x}\]
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 \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = x^{100} + x^{99} + . . . + x + 1\] then \[f'\left( 1 \right)\] is equal to
Mark the correct alternative in each of the following:
If\[y = \frac{\sin x + \cos x}{\sin x - \cos x}\] then \[\frac{dy}{dx}\]at x = 0 is
Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.
