Advertisements
Advertisements
Question
\[\text{ If } y = \left( \frac{2 - 3 \cos x}{\sin x} \right), \text{ find } \frac{dy}{dx} at x = \frac{\pi}{4}\]
Advertisements
Solution
\[\frac{dy}{dx} = \frac{d}{dx}\left( \frac{2 - 3 \cos x}{\sin x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2}{\sin x} \right) - \frac{d}{dx}\left( \frac{3 \cos x}{\sin x} \right)\]
\[ = 2\frac{d}{dx}\left( \cos ec x \right) - 3\frac{d}{dx}\left( \cot x \right)\]
\[ = - 2 \cos ec x \cot x + 3 \cos e c^2 x\]
\[\frac{dy}{dx} at x=\frac{\pi}{4}= - 2 \cos ec \frac{\pi}{4} \cot \frac{\pi}{4} + 3 \cos e c^2 \frac{\pi}{4}\]
\[ = - 2\left( \sqrt{2} \right)\left( 1 \right) + 3 \left( \sqrt{2} \right)^2 \]
\[ = - 2\sqrt{2} + 6\]
\[ = 6 - 2\sqrt{2}\]
\[\]
APPEARS IN
RELATED QUESTIONS
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):
`(ax + b)/(px^2 + qx + r)`
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):
`(sin x + cos x)/(sin x - cos x)`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of the following function at the indicated point:
sin x at x =\[\frac{\pi}{2}\]
Find the derivative of the following function at the indicated point:
\[\frac{2}{x}\]
\[\frac{x^2 - 1}{x}\]
(x + 2)3
Differentiate each of the following from first principle:
e−x
Differentiate of the following from first principle:
x sin x
Differentiate of the following from first principle:
sin (2x − 3)
Differentiate each of the following from first principle:
\[\sqrt{\sin 2x}\]
Differentiate each of the following from first principle:
\[\frac{\cos x}{x}\]
\[\tan \sqrt{x}\]
\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
cos (x + a)
x3 sin x
(x3 + x2 + 1) sin x
\[\frac{2^x \cot x}{\sqrt{x}}\]
x2 sin x log x
\[e^x \log \sqrt{x} \tan x\]
x−3 (5 + 3x)
\[\frac{e^x - \tan x}{\cot x - x^n}\]
\[\frac{1}{a x^2 + bx + c}\]
\[\frac{x^2 - x + 1}{x^2 + x + 1}\]
\[\frac{a + \sin x}{1 + a \sin x}\]
\[\frac{1 + 3^x}{1 - 3^x}\]
\[\frac{x}{1 + \tan x}\]
\[\frac{x^5 - \cos x}{\sin x}\]
\[\frac{ax + b}{p x^2 + qx + r}\]
Write the value of \[\frac{d}{dx}\left( \log \left| x \right| \right)\]
Mark the correct alternative in of the following:
If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\]
Mark the correct alternative in each of the following:
If\[f\left( x \right) = \frac{x^n - a^n}{x - a}\] then \[f'\left( a \right)\]
Mark the correct alternative in of the following:
If f(x) = x sinx, then \[f'\left( \frac{\pi}{2} \right) =\]
Find the derivative of 2x4 + x.
