Question:
Differentiate:
$x^{4} \tan x$
Solution:
To find: Differentiation of $x^{4} \tan x$
Formula used: (i) (uv)' = u'v + uv' (Leibnitz or product rule)
(ii)
$\frac{d x^{n}}{d x}=n x^{n-1}$
(iii)
$\frac{d \tan x}{d x}=\sec ^{2} x$
Let us take $u=x^{4}$ and $v=\tan x$
$u^{\prime}=\frac{d u}{d x}=\frac{d x^{4}}{d x}=4 x^{3}$
$v^{\prime}=\frac{d v}{d x}=\frac{d \tan x}{d x}=\sec ^{2} x$
Putting the above obtained values in the formula:-
$(U V)^{\prime}=U^{\prime} V+U V^{\prime}$
$\left(x^{4} \tan x\right)^{\prime}=4 x^{3} \times \tan x+x^{4} \times \sec ^{2} x$
$=4 x^{3} \tan x+x^{4} \sec ^{2} x$
$=x^{3}\left(4 \tan x+x \sec ^{2} x\right)$
Ans) $x^{3}\left(4 \tan x+x \sec ^{2} x\right)$
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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,
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