Advertisements
Advertisements
प्रश्न
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Advertisements
उत्तर
\[\frac{dy}{dx} = \frac{d}{dx}\left( \frac{2 - 3 \cos x}{\sin x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2}{\sin x} \right) - \frac{d}{dx}\left( \frac{3 \cos x}{\sin x} \right)\]
\[ = 2\frac{d}{dx}\left( \cos ec x \right) - 3\frac{d}{dx}\left( \cot x \right)\]
\[ = - 2 \cos ec x \cot x + 3 \cos e c^2 x\]
\[\frac{dy}{dx} at x=\frac{\pi}{4}= - 2 \cos ec \frac{\pi}{4} \cot \frac{\pi}{4} + 3 \cos e c^2 \frac{\pi}{4}\]
\[ = - 2\left( \sqrt{2} \right)\left( 1 \right) + 3 \left( \sqrt{2} \right)^2 \]
\[ = - 2\sqrt{2} + 6\]
\[ = 6 - 2\sqrt{2}\]
\[\]
APPEARS IN
संबंधित प्रश्न
Find the derivative of x–3 (5 + 3x).
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):
cosec x cot 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):
`(sec x - 1)/(sec x + 1)`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) = tan x at x = 0
Find the derivative of the following function at the indicated point:
(x + 2)3
x ex
Differentiate of the following from first principle:
− x
Differentiate of the following from first principle:
(−x)−1
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:
\[e^\sqrt{2x}\]
\[\sqrt{\tan x}\]
\[\sin \sqrt{2x}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]
If for f (x) = λ x2 + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ.
x2 ex log x
xn loga x
\[\frac{2^x \cot x}{\sqrt{x}}\]
(ax + b) (a + d)2
\[\frac{x^2 + 1}{x + 1}\]
\[\frac{x + e^x}{1 + \log x}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x \sin x}{1 + \cos x}\]
\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]
\[\frac{a + b \sin x}{c + d \cos x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\]
If f (x) = \[\log_{x_2}\]write the value of f' (x).
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
`(a + b sin x)/(c + d cos x)`
