f’ Complete Derivative Symbols Generator

Master derivative calculus with f’, ∂f/∂x, f”, ∂²f/∂x² symbols. Perfect for calculus students, mathematicians, physicists, and engineers with interactive differentiation calculator.

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🧮 Derivative Calculator

Evaluate derivative expressions, solve differentiation problems, and perform calculus operations with step-by-step solutions.

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Complete Derivative Calculus Symbols & Operators

f’ Basic Derivative Symbols

FIRST DERIVATIVE

SECOND DERIVATIVE

THIRD DERIVATIVE

FOURTH DERIVATIVE

FIFTH DERIVATIVE

SIXTH DERIVATIVE

SEVENTH DERIVATIVE

EIGHTH DERIVATIVE

NINTH DERIVATIVE

TENTH DERIVATIVE

NTH DERIVATIVE

TIME DERIVATIVE

SECOND TIME DERIV

∂ Partial Derivatives

PARTIAL DERIVATIVE X

PARTIAL DERIVATIVE Y

PARTIAL DERIVATIVE Z

PARTIAL DERIVATIVE T

SECOND PARTIAL X

SECOND PARTIAL Y

THIRD PARTIAL X

MIXED PARTIAL XY

MIXED PARTIAL YX

THIRD MIXED

TRIPLE MIXED

FOURTH PARTIAL

RADIAL PARTIAL

ANGULAR PARTIAL

AZIMUTHAL PARTIAL

🌊 Vector Calculus Derivatives

GRADIENT

DIVERGENCE

CURL

LAPLACIAN

LAPLACIAN ALT

LAPLACIAN VECTOR

GRADIENT U

DIVERGENCE V

LAPLACIAN CURL

GRADIENT PRODUCT

DIVERGENCE PRODUCT

CURL PRODUCT

DIVERGENCE CURL

🎯 Advanced Derivatives

FUNCTIONAL DERIVATIVE

FRECHET DERIVATIVE

FIRST DERIVATIVE FX

SECOND DERIVATIVE FX

THIRD DERIVATIVE FX

FOURTH DERIVATIVE FX

PARTIAL TIME

SECOND PARTIAL TIME

PROPER TIME PARTIAL

WAVE FUNCTION SECOND

DENSITY TIME DERIV

PRESSURE VOLUME

TEMPERATURE ENTROPY

⚛️ Specialized Derivatives

ACCELERATION

JERK

SNAP

CRACKLE

POP

CHEMICAL POTENTIAL

FREQUENCY PARTIAL

WAVELENGTH PARTIAL

ANGULAR FREQUENCY

WAVE NUMBER

ENERGY PARTIAL

MASS PARTIAL

⚛️ Physics Derivatives

VELOCITY

ACCELERATION

JERK

POWER

FORCE DERIVATIVE

CONTINUITY

SCHRÖDINGER

MAXWELL

🧮 Differential Operators

DIFFERENTIAL

DIFFERENTIAL X

DIFFERENTIAL Y

DIFFERENTIAL Z

DIFFERENTIAL T

SECOND DIFFERENTIAL

VARIATION

PARTIAL SYMBOL

Derivative Calculus Expressions & Examples

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f'(x)

Table of Contents

f’ Complete Derivative Symbols Reference Table
💡 Quick Derivative Symbol Reference
Derivative Calculus Expressions and Applications
f' Derivative Font Generator Error
Author

f’ Complete Derivative Symbols Reference Table

Master the complete collection of derivative calculus symbols with our comprehensive reference table. Click any symbol to copy it instantly for use in your calculus proofs, physics equations, and engineering calculations. For additional study support, check out our Exam Prep Guides to strengthen your exam preparation.

Symbol	Name	HTML Code	Unicode	Category	Usage
f’ Basic Derivatives
f’	First Derivative	f′	U+0066 U+2032	Differential Calculus	f'(x) = df/dx
f”	Second Derivative	f″	U+0066 U+2033	Differential Calculus	f”(x) = d²f/dx²
f”’	Third Derivative	f′′′	U+0066 U+2034	Differential Calculus	f”'(x) = d³f/dx³
f⁽⁴⁾	Fourth Derivative	f&sup4;	U+0066 U+207D U+2074 U+207E	Differential Calculus	f⁽⁴⁾(x) = d⁴f/dx⁴
f⁽⁵⁾	Fifth Derivative	f&sup5;	U+0066 U+207D U+2075 U+207E	Differential Calculus	f⁽⁵⁾(x) = d⁵f/dx⁵
∂ Partial Derivatives
∂	Partial Derivative	∂	U+2202	Differential	∂f/∂x
∂f/∂x	Partial Derivative X	∂f/∂x	U+2202 U+0066 U+002F U+2202 U+0078	Partial Calculus	∂f/∂x
∂²f/∂x²	Second Partial X	∂²f/∂x²	U+2202 U+00B2 U+0066 U+002F U+2202 U+0078 U+00B2	Partial Calculus	∂²f/∂x²
∂³f/∂x³	Third Partial X	∂³f/∂x³	U+2202 U+00B3 U+0066 U+002F U+2202 U+0078 U+00B3	Partial Calculus	∂³f/∂x³
∂²f/∂x∂y	Mixed Partial Derivative	∂²f/∂x∂y	U+2202 U+00B2 U+0066 U+002F U+2202 U+0078 U+2202 U+0079	Partial Calculus	∂²f/∂x∂y
🌊 Vector Calculus
∇	Nabla (Del)	∇	U+2207	Vector Operator	∇f
∇f	Gradient	∇f	U+2207 U+0066	Vector Operator	∇f
∇·F	Divergence	∇⋅F	U+2207 U+22C5 U+0046	Vector Operator	∇·F
∇×F	Curl	∇×F	U+2207 U+00D7 U+0046	Vector Operator	∇×F
∇²f	Laplacian	∇²f	U+2207 U+00B2 U+0066	Vector Operator	∇²f
Δ	Laplacian	Δ	U+2206	Vector Operator	Δf = ∇²f
🎯 Functional Analysis
δf/δx	Functional Derivative	δf/δx	U+03B4 U+0066 U+002F U+03B4 U+0078	Functional Calculus	δf/δx
Df	Frechet Derivative	Df	U+0044 U+0066	Differential Calculus	Df(x)
δ	Variation	δ	U+03B4	Calculus of Variations	δf
🧮 Differential Operators
d	Differential	d	U+0064	Differential	dx
dx	Differential X	dx	U+0064 U+0078	Differential	dx
dy	Differential Y	dy	U+0064 U+0079	Differential	dy
dz	Differential Z	dz	U+0064 U+007A	Differential	dz
dt	Differential T	dt	U+0064 U+0074	Differential	dt
d²x	Second Differential	d²x	U+0064 U+00B2 U+0078	Differential	d²x
⚛️ Physics Derivatives
dv/dt	Velocity (Physics)	dv/dt	U+0064 U+0076 U+002F U+0064 U+0074	Physics	dv/dt = a (acceleration)
d²v/dt²	Acceleration	d²v/dt²	U+0064 U+00B2 U+0076 U+002F U+0064 U+0074 U+00B2	Physics	d²v/dt² = a
d³v/dt³	Jerk	d³v/dt³	U+0064 U+00B3 U+0076 U+002F U+0064 U+0074 U+00B3	Physics	d³v/dt³ = da/dt
dE/dt	Power	dE/dt	U+0064 U+0045 U+002F U+0064 U+0074	Physics	dE/dt = P
∂ρ/∂t	Continuity Equation	∂ρ/∂t	U+2202 U+03C1 U+002F U+2202 U+0074	Physics	∂ρ/∂t + ∇·(ρv) = 0
∇²ψ	Schrödinger Equation	∇²ψ	U+2207 U+00B2 U+03C8	Quantum Physics	-ℏ²/2m ∇²ψ + Vψ = iℏ ∂ψ/∂t
∂B/∂t	Maxwell’s Equation	∂B/∂t	U+2202 U+0042 U+002F U+2202 U+0074	Electromagnetism	∇×E = -∂B/∂t

💡 Quick Derivative Symbol Reference

Basic Derivatives

f’ First • f” Second • f”’ Third • f⁽⁴⁾ Fourth

Partial Derivatives

∂ Partial • ∂²f/∂x² Second • ∂²f/∂x∂y Mixed

Vector Calculus

∇f Gradient • ∇·F Divergence • ∇×F Curl

Advanced Derivatives

δf/δx Functional • Df Frechet • ∇²f Laplacian

Derivative Calculus Expressions and Applications

f'(x) = lim h→0 [f(x+h) – f(x)]/h
Derivative definition – fundamental theorem of calculus

∂f/∂x
Partial derivative – multivariate calculus

∂²f/∂x²
Second partial derivative – Hessian component

∂³f/∂x³
Third partial derivative – higher-order calculus

∂²f/∂x∂y
Mixed partial derivative – cross derivatives

∇f
Gradient vector – steepest ascent direction

∇·F
Divergence – vector field expansion/contraction

∇×F
Curl – vector field rotation measure

∇²f = ∂²f/∂x² + ∂²f/∂y² + ∂²f/∂z²
Laplacian operator – appears in heat, wave, and Schrödinger equations

δf/δx
Functional derivative – calculus of variations and optimal control

f’ , f” , f”’ , f⁽⁴⁾
Higher-order derivatives – essential for Taylor series expansions

Df(x) = lim h→0 [f(x+h) – f(x)]/h
Fréchet derivative – generalization to Banach spaces

∂²f/∂x∂y = ∂²f/∂y∂x
Schwarz’s theorem – equality of mixed partial derivatives for C² functions

∇·∇f = ∇²f
Laplacian alternative notation – divergence of gradient

f'(x) = df/dx
Leibniz notation – derivative as infinitesimal ratio

d²y/dx² = 0
Inflection point condition – second derivative test

∇f · ∇g = 0
Orthogonal gradients – level curves are perpendicular

∂u/∂t + u ∂u/∂x = 0
Advection equation – transport of conserved quantities

Author

Manish Kumar
Manish holds a B.Tech in Electrical and Electronics Engineering (EEE) and an M.Tech in Power Systems, with over 10 years of experience in Metro Rail Systems, specializing in advanced rail infrastructure.
He is also a NASM-certified fitness and nutrition coach with more than a decade of experience in weightlifting and fat loss coaching. With expertise in gym-based training, lifting techniques, and biomechanics, Manish combines his technical mindset with his passion for fitness.