How to Use the Derivative Rules Calculator
Select a function type and enter the required coefficients to instantly display the function, its derivative formula, and the rule applied. Covers power, exponential, natural log, sine, cosine, and tangent functions.
Basic Derivative Rules Summary
- Power Rule: d/dx[axⁿ] = a·n·x^(n-1)
- Exponential: d/dx[a·e^(bx)] = a·b·e^(bx)
- Natural Log: d/dx[a·ln(x)] = a/x
- Sine: d/dx[a·sin(bx)] = a·b·cos(bx)
- Cosine: d/dx[a·cos(bx)] = −a·b·sin(bx)
- Tangent: d/dx[a·tan(x)] = a·sec²(x)
Frequently Asked Questions
How do I remember the power rule?
Bring the exponent to the front and subtract 1 from it: d/dx[x³] = 3x². Simple and applies to any polynomial.
Why is d/dx[eˣ] = eˣ?
The natural exponential function eˣ is unique in being its own derivative — a property that follows directly from the definition of e as the limit of (1 + 1/n)ⁿ as n→∞.
What is the chain rule?
For composite f(g(x)): d/dx[f(g(x))] = f'(g(x))·g'(x). Example: d/dx[sin(3x)] = cos(3x)·3 = 3cos(3x).