Question:
(3x + 5) (1 + tan x)
Solution:
Given $(3 x+5)(1+\tan x)$
Let $y=(3 x+5)(1+\tan x)$
Applying product rule of differentiation that is
$\Rightarrow \frac{\mathrm{d}}{\mathrm{dx}}(\mathrm{t} \cdot \mathrm{y})=\mathrm{y} \cdot \frac{\mathrm{d} \mathrm{t}}{\mathrm{dx}}+\mathrm{t} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}$
$\Rightarrow y=(3 x+5)(1+\tan x)$
$\Rightarrow \frac{d y}{d x}=(1+\tan x) \frac{d}{d x}(3 x+5)+(3 x+5) \frac{d}{d x}(1+\tan x)$
$\Rightarrow \frac{d y}{d x}=3(1+\tan x)+(3 x+5) \sec ^{2} x$
$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=3 \mathrm{x} \sec ^{2} \mathrm{x}+5 \sec ^{2} \mathrm{x}+3+3 \tan \mathrm{x}$ (by using product rule)
Hence, the required answer is $3 x \sec ^{2} x+5 \sec ^{2} x+3 \tan x+3$
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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,
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