Derivative Calculator
Calculate derivatives of common functions with step-by-step solutions. Perfect for calculus students, teachers, and professionals working with mathematical analysis.
Derivative Calculator
Calculate derivatives of common functions with step-by-step solutions
Select Function Type
Common Derivative Rules
• Power Rule: d/dx(xⁿ) = nxⁿ⁻¹
• Constant Rule: d/dx(c) = 0
• Exponential: d/dx(eˣ) = eˣ
• Logarithmic: d/dx(ln(x)) = 1/x
• Trigonometric: d/dx(sin(x)) = cos(x)
Common Derivatives
Understanding Derivatives
A derivative represents the rate of change of a function with respect to its variable. In calculus, derivatives are fundamental tools used to analyze how functions behave and change over their domain.
The derivative f'(x) of a function f(x) gives us the slope of the tangent line to the graph of f at any point x. This has numerous applications in physics, engineering, economics, and many other fields.
Our calculator supports several common function types including polynomials, power functions, exponential functions, trigonometric functions, and logarithmic functions.
How to Use This Calculator
Key Derivative Rules
Power Rule
For f(x) = xⁿ, the derivative is f'(x) = nxⁿ⁻¹. This is one of the most fundamental rules.
Trigonometric
d/dx(sin(x)) = cos(x), d/dx(cos(x)) = -sin(x), d/dx(tan(x)) = sec²(x).
Exponential & Log
d/dx(eˣ) = eˣ, d/dx(ln(x)) = 1/x, d/dx(aˣ) = aˣ × ln(a).