🧮 Fraction Derivative Calculator
Compute derivatives of rational functions with step‑by‑step explanations. Uses the quotient rule, power rule, and simplifies automatically. Plot both function and its derivative.
Step 1: Enter function
(only first derivative is active)
📘 How to enter fractions
Use / for division, ^ for power. Examples: (x^3+1)/(x-2), (sin(x)+x)/cos(x) (basic functions work).
Step 2: Options
⚡ Differentiation rules
Quotient rule: (f/g)’ = (f’·g − f·g’)/g². Power, product, chain rules are applied automatically.
Derivative result
Derivative
Steps
Graph
f'(x) =
(2x·(x-1) – (x²+2)·1)/(x-1)²
f(x) = (x²+2)/(x-1)
Simplified form
(x² -2x -2)/(x-1)²
At x = 2
-2
Type
rational
Domain excl.
x = 1
Step‑by‑step differentiation
1. Identify numerator N = x²+2, denominator D = x-1
2. Derivative N’ = 2x, D’ = 1
3. Apply quotient rule: (N’·D – N·D’) / D²
4. = (2x·(x-1) – (x²+2)·1) / (x-1)²
5. Expand numerator: 2x² – 2x – x² – 2 = x² – 2x – 2
6. Result: (x² – 2x – 2) / (x-1)²
2. Derivative N’ = 2x, D’ = 1
3. Apply quotient rule: (N’·D – N·D’) / D²
4. = (2x·(x-1) – (x²+2)·1) / (x-1)²
5. Expand numerator: 2x² – 2x – x² – 2 = x² – 2x – 2
6. Result: (x² – 2x – 2) / (x-1)²
Function (blue) & derivative (red)
f(x) and f'(x) over selected range
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