Calculate the instantaneous rate of change (derivative) of a function.
Differentiation Settings
Concept
"Think of the derivative as a speedometer for your function. At any point 'x', it tells you exactly how fast the function's value is rising or falling."
Resulting Derivative
2x + 5
f'(x) - Symbolic
f'(a) - Numeric Value---
Evaluation Pointx = 1
About this calculator
What is a Derivative?
The derivative of a function measures the sensitivity to change of the output value with respect to its input value. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point. It's the central concept of differential calculus.
💡
Pro Tips
The Power Rule: d/dx [xⁿ] = nxⁿ⁻¹.
The derivative of a constant is always 0.
If f'(x) > 0, the function is increasing; if f'(x) < 0, it is decreasing.
!
Fun Facts
"Isaac Newton and Gottfried Wilhelm Leibniz independently developed calculus in the late 17th century."
"The notation f'(x) was introduced by Joseph-Louis Lagrange."
"Derivatives are used in economics to calculate 'marginal cost' and 'marginal revenue'."
