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 x5 (3 – 6x–9).
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):
`4sqrtx - 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):
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):
`(sin(x + a))/ cos x`
Find the derivative of f (x) = 99x at x = 100
Find the derivative of f (x) = tan x at x = 0
\[\frac{x + 1}{x + 2}\]
Differentiate of the following from first principle:
sin (x + 1)
Differentiate of the following from first principle:
\[\cos\left( x - \frac{\pi}{8} \right)\]
Differentiate each of the following from first principle:
sin x + cos x
Differentiate each of the following from first principle:
\[e^\sqrt{2x}\]
Differentiate each of the following from first principle:
\[a^\sqrt{x}\]
\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\]
\[\frac{( x^3 + 1)(x - 2)}{x^2}\]
\[\frac{a \cos x + b \sin x + c}{\sin x}\]
2 sec x + 3 cot x − 4 tan x
\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\]
Find the slope of the tangent to the curve f (x) = 2x6 + x4 − 1 at x = 1.
xn loga x
sin x cos x
(1 − 2 tan x) (5 + 4 sin x)
sin2 x
\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]
x5 (3 − 6x−9)
Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.
(3x2 + 2)2
(ax + b)n (cx + d)n
\[\frac{x}{1 + \tan x}\]
\[\frac{e^x}{1 + x^2}\]
\[\frac{e^x + \sin x}{1 + \log x}\]
\[\frac{1 + \log x}{1 - \log x}\]
Write the value of \[\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}\]
Mark the correct alternative in of the following:
If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]
(ax2 + cot x)(p + q cos x)
