Kalkulator Turunan

Hitung turunan f'(x) dan visualisasikan garis singgung secara dinamis. Geser slider untuk melihat kemiringan berubah di titik mana pun.

∂ Derivative Graph + Tangent Line
∂
Enter a function and compute its derivative

Coba contoh ini

Cubic
f(x) = x³ - 3x
Trigonometric
f(x) = sin(x)
Product Rule
f(x) = x²·eˣ
Chain Rule
f(x) = ln(x²+1)
📚 What is a Derivative?

Understanding Derivatives

The derivative f'(x) measures the rate of change of a function at any given point. Geometrically, it represents the slope of the tangent line to the curve at that point.

f'(x) = limh→0 [f(x+h) - f(x)] / h

Key interpretations:

  • f'(x) > 0 → function is increasing at x
  • f'(x) < 0 → function is decreasing at x
  • f'(x) = 0 → possible maximum, minimum, or inflection point

Common derivative rules:

  • Power Rule: d/dx(xⁿ) = n·xⁿ⁻¹
  • Product Rule: d/dx(f·g) = f'g + fg'
  • Chain Rule: d/dx(f(g(x))) = f'(g(x))·g'(x)
❓ FAQ

Frequently Asked Questions

The tangent line touches the curve at exactly one point and has the same slope as the curve at that point. Its slope equals f'(x) — the derivative value at that x.
When f'(x) = 0, the function has a horizontal tangent. This could be a local maximum, minimum, or saddle point. Use the second derivative f''(x) to classify.
The calculator uses symbolic differentiation (Math.js) and simplifies the result automatically. The expression may look different but is mathematically equivalent.