Calculus Mastery Suite
Differentiation Solver
Find the instantaneous rate of change for any polynomial. Master the power rule and solve derivatives in seconds.
Differentiation Solver
Power Rule: d/dx (axⁿ)
x
Derivative (dy/dx)6x
The Power Rule
To differentiate a power of x, multiply the expression by the original power (n) and then decrease the power by one. Mathematically: nxⁿ⁻¹.
What is a Derivative?
The derivative of a function measures how the function changes as its input changes. In geometry, the derivative at a point is the slope of the tangent line to the graph of the function at that point.
Notation Styles
- Leibniz's Notation:
dy/dx - Lagrange's Notation:
f'(x) - Newton's Notation:
ẏ
Applications
Physics: Calculating velocity from position.
Economics: Finding marginal cost and revenue.
Engineering: Optimizing design parameters.
Biology: Modeling population growth rates.
Optimization Fact
To find the maximum or minimum value of a function, you set its derivative to zero and solve for x.