\[\frac{x^2 \cos\frac{\pi}{4}}{\sin x}\]

\[\frac{x^2 \cos \frac{\pi}{4}}{\sin x} = x^2 \cos \frac{\pi}{4} cosec x\]\[\text{ Let } u = x^2 ; v = \cos \frac{\pi}{4}; w = cosec x\]\[\text{ Then }, u' = 2x; v' = 0; w' = - cosec x \cot x\]\[\text{ Using the product rule }:\]\[\frac{d}{dx}\left( uvw \right) = u'vw + uv'w + uvw'\]\[\frac{d}{dx}\left( x^2 \cos \frac{\pi}{4} cosec x \right) = 2x \cos \frac{\pi}{4}cosec x + x^2 . 0 . cosec x + x^2 \cos \frac{\pi}{4}\left( - \cosec x \cot x \right)\]\[ = \cos \frac{\pi}{4}\left( 2x cosec x - x^2 cosec x \cot x \right)\]\[ = \cos \frac{\pi}{4}\left( \frac{2x}{\sin x} - x^2 \frac{\cot x}{\sin x} \right)\]\[\]

X 2 Cos π 4 Sin X - Mathematics

Question

$\frac{x^{2} \cos \frac{π}{4}}{\sin x}$

Solution

$\frac{x^{2} \cos \frac{π}{4}}{\sin x} = x^{2} \cos \frac{π}{4} c o s e c x$
$Let u = x^{2}; v = \cos \frac{π}{4}; w = c o s e c x$
$Then, u^{'} = 2 x; v^{'} = 0; w^{'} = - c o s e c x \cot x$
$Using the product rule :$
$\frac{d}{d x} (u v w) = u^{'} v w + u v^{'} w + u v w^{'}$
$\frac{d}{d x} (x^{2} \cos \frac{π}{4} c o s e c x) = 2 x \cos \frac{π}{4} c o s e c x + x^{2} . 0 . c o s e c x + x^{2} \cos \frac{π}{4} (- \cosec x \cot x)$
$= \cos \frac{π}{4} (2 x c o s e c x - x^{2} c o s e c x \cot x)$
$= \cos \frac{π}{4} (\frac{2 x}{\sin x} - x^{2} \frac{\cot x}{\sin x})$

shaalaa.com

The Concept of Derivative - Algebra of Derivative of Functions

Is there an error in this question or solution?

Q 19 Q 18 Q 20

Chapter 30: Derivatives - Exercise 30.4 [Page 39]

APPEARS IN

RD Sharma Mathematics [English] Class 11

Chapter 30 Derivatives
Exercise 30.4 | Q 19 | Page 39

Video TutorialsVIEW ALL [1]

view
Video Tutorials For All Subjects
The Concept of Derivative - Algebra of Derivative of Functions

video tutorial00:07:37

RELATED QUESTIONS

Find the derivative of 99x at x = 100.

Find the derivative of x at x = 1.

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):

(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):

$\frac{\cos x}{1 + \sin x}$

Find the derivative of f (x) = cos x at x = 0

$\frac{1}{\sqrt{3 - x}}$

(x² + 1) (x − 5)

$\sqrt{2 x^{2} + 1}$

Differentiate of the following from first principle:

e^3x

Differentiate of the following from first principle:

x sin x

Differentiate each of the following from first principle:

$\sqrt{\sin 2 x}$

Differentiate each of the following from first principle:

$e^{x^{2} + 1}$

Differentiate each of the following from first principle:

$3^{x^{2}}$

tan² x

$(x + \frac{1}{x}) (\sqrt{x} + \frac{1}{\sqrt{x}})$

a₀ xⁿ + a₁ xⁿ⁻¹ + a₂ xⁿ⁻² + ... + a_n₋₁ x + a_n.

$\frac{(x + 5) (2 x^{2} - 1)}{x}$

$If y = {(\sin \frac{x}{2} + \cos \frac{x}{2})}^{2}, find \frac{d y}{d x} a t x = \frac{π}{6} .$

xⁿ tan x

sin x cos x

$\frac{2^{x} \cot x}{\sqrt{x}}$

$e^{x} \log \sqrt{x} \tan x$

(ax + b) (a + d)²

$\frac{x^{2} + 1}{x + 1}$

$\frac{\sin x - x \cos x}{x \sin x + \cos x}$

$\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}$

$\frac{1 + 3^{x}}{1 - 3^{x}}$

$\frac{1 + \log x}{1 - \log x}$

$\frac{a + b \sin x}{c + d \cos x}$

$\frac{x}{\sin^{n} x}$

If x < 2, then write the value of $\frac{d}{d x} (\sqrt{x^{2} - 4 x + 4)}$

Write the value of $\frac{d}{d x} {(x + | x |) | x |}$

Mark the correct alternative in of the following:

If $y = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . .$ then $\frac{d y}{d x} =$

Mark the correct alternative in of the following:
If $f (x) = 1 + x + \frac{x^{2}}{2} + . . . + \frac{x^{100}}{100}$ then $f^{'} (1)$ is equal to

Mark the correct alternative in each of the following:

If $f (x) = \frac{x^{n} - a^{n}}{x - a}$ then $f^{'} (a)$

Find the derivative of x² cosx.

(ax² + cot x)(p + q cos x)

X 2 Cos π 4 Sin X - Mathematics

Advertisements

Advertisements

Question

Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

X 2 Cos π 4 Sin X - Mathematics

Advertisements

Advertisements

Question

SolutionShow Solution

APPEARS IN

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Select a course

Solution