Derivative Calculator
Calculate derivatives of mathematical functions with step-by-step solutions
Differentiation Rules
Basic Rules
Power Rule: (x^n)' = nx^(n-1)
Constant Rule: (c)' = 0
Sum Rule: (f + g)' = f' + g'
Product Rule: (fg)' = f'g + fg'
Quotient Rule: (f/g)' = (f'g - fg')/g²
Special Functions
sin(x)' = cos(x)
cos(x)' = -sin(x)
tan(x)' = sec²(x)
e^x' = e^x
ln(x)' = 1/x
Applications
Physics
- Velocity and acceleration
- Force and momentum
- Rate of change calculations
- Optimization problems
Economics
- Marginal cost and revenue
- Elasticity of demand
- Growth rate analysis
- Optimization of profit
What is a Derivative?
A derivative represents the rate of change of a function with respect to its variable. Geometrically, it gives the slope of the tangent line to the function at any point, making it fundamental for understanding how quantities change over time or space.