(ax2 + cot x) (p + q cos x)
Given $y=\left(a x^{2}+\cot x\right)(p+q \cos x)$
Applying product rule of differentiation that
$\Rightarrow \frac{d}{d x}(t . y)=y \cdot \frac{d t}{d x}+t \cdot \frac{d y}{d x}$
$\Rightarrow y=\left(a x^{2}+\cot x\right)(p+q \cos x)$
Now splitting the differentials,
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=(\mathrm{p}+\mathrm{q} \cos \mathrm{x}) \frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ax}^{2}+\cot \mathrm{x}\right)+\left(\mathrm{ax}^{2}+\cot \mathrm{x}\right) \frac{\mathrm{d}}{\mathrm{dx}}(\mathrm{p}+\mathrm{q} \cos \mathrm{x})$
On differentiation we get
$\Rightarrow \frac{d y}{d x}=(p+q \cos x)\left(2 a x-\operatorname{cosec}^{2} x\right)+\left(a x^{2}+\cot x\right)(-q \sin x)$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=(\mathrm{p}+\mathrm{q} \cos \mathrm{x})\left(2 \mathrm{ax}-\operatorname{cosec}^{2} \mathrm{x}\right)-\mathrm{q} \sin \mathrm{x}\left(\mathrm{ax}^{2}+\cot \mathrm{x}\right)$
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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,