Question:
Differentiate the functions with respect to x.
$2 \sqrt{\cot \left(x^{2}\right)}$
Solution:
$\frac{d}{d x}\left[2 \sqrt{\cot \left(x^{2}\right)}\right]$
$=2 \cdot \frac{1}{2 \sqrt{\cot \left(x^{2}\right)}} \times \frac{d}{d x}\left[\cot \left(x^{2}\right)\right]$
$=\sqrt{\frac{\sin \left(x^{2}\right)}{\cos \left(x^{2}\right)}} \times-\operatorname{cosec}^{2}\left(x^{2}\right) \times \frac{d}{d x}\left(x^{2}\right)$
$=-\sqrt{\frac{\sin \left(x^{2}\right)}{\cos \left(x^{2}\right)}} \times \frac{1}{\sin ^{2}\left(x^{2}\right)} \times(2 x)$
$=\frac{-2 x}{\sqrt{\cos x^{2}} \sqrt{\sin x^{2}} \sin x^{2}}$
$=\frac{-2 \sqrt{2} x}{\sqrt{2 \sin x^{2} \cos x^{2}} \sin x^{2}}$
$=\frac{-2 \sqrt{2} x}{\sin x^{2} \sqrt{\sin 2 x^{2}}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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