Differentiate the following with respect to x:
$\sqrt{\sin x^{3}}$
To Find: Differentiation
NOTE : When 2 functions are in the product then we used product rule i.e
$\frac{\mathrm{d}(\mathrm{u} \cdot \mathrm{v})}{\mathrm{dx}}=\mathrm{V} \frac{\mathrm{du}}{\mathrm{dx}}+\mathrm{u} \frac{\mathrm{dv}}{\mathrm{dx}}$c
Formula used: $\frac{d}{d x}\left(\sqrt{\sin u^{a}}\right)=\frac{1}{2 \sqrt{\sin u^{a}}} \times \frac{d}{d x}\left(\sin u^{a}\right) \times \frac{d}{d x}\left(u^{a}\right)$
Let us take $y=\sqrt{\sin x^{3}}$
So, by using the above formula, we have
$\frac{d}{d x} \sqrt{\sin x^{3}}=\frac{1}{2 \sqrt{\sin x^{3}}} \times \frac{d}{d x}\left(\sin x^{3}\right) \times \frac{d}{d x}\left(x^{3}\right)=\frac{1}{2 \sqrt{\sin x^{3}}} \times\left(\cos x^{3}\right) \times 3 x^{2}=\frac{3 x^{2}\left(\cos x^{3}\right)}{2 \sqrt{\sin x^{3}}}$
Differentiation of $y=\sqrt{\sin x^{3}}$ is $\frac{3 x^{2}\left(\cos x^{3}\right)}{2 \sqrt{\sin x^{3}}}$
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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,