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.
🧮 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
f'(x)
Table of Contents
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
Derivative definition – fundamental theorem of calculus
∂f/∂x
Partial derivative – multivariate calculus
Partial derivative – multivariate calculus
∂²f/∂x²
Second partial derivative – Hessian component
Second partial derivative – Hessian component
∂³f/∂x³
Third partial derivative – higher-order calculus
Third partial derivative – higher-order calculus
∂²f/∂x∂y
Mixed partial derivative – cross derivatives
Mixed partial derivative – cross derivatives
∇f
Gradient vector – steepest ascent direction
Gradient vector – steepest ascent direction
∇·F
Divergence – vector field expansion/contraction
Divergence – vector field expansion/contraction
∇×F
Curl – vector field rotation measure
Curl – vector field rotation measure
∇²f = ∂²f/∂x² + ∂²f/∂y² + ∂²f/∂z²
Laplacian operator – appears in heat, wave, and Schrödinger equations
Laplacian operator – appears in heat, wave, and Schrödinger equations
δf/δx
Functional derivative – calculus of variations and optimal control
Functional derivative – calculus of variations and optimal control
f’ , f” , f”’ , f⁽⁴⁾
Higher-order derivatives – essential for Taylor series expansions
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
Fréchet derivative – generalization to Banach spaces
∂²f/∂x∂y = ∂²f/∂y∂x
Schwarz’s theorem – equality of mixed partial derivatives for C² functions
Schwarz’s theorem – equality of mixed partial derivatives for C² functions
∇·∇f = ∇²f
Laplacian alternative notation – divergence of gradient
Laplacian alternative notation – divergence of gradient
f'(x) = df/dx
Leibniz notation – derivative as infinitesimal ratio
Leibniz notation – derivative as infinitesimal ratio
d²y/dx² = 0
Inflection point condition – second derivative test
Inflection point condition – second derivative test
∇f · ∇g = 0
Orthogonal gradients – level curves are perpendicular
Orthogonal gradients – level curves are perpendicular
∂u/∂t + u ∂u/∂x = 0
Advection equation – transport of conserved quantities
Advection equation – transport of conserved quantities