अवकलज और अवकलन कैलकुलेटर
यह कैलकुलेटर घात नियम से बहुपदों का अवकलन करता है और हर पद का अवकलज तथा दूसरा अवकलज दिखाता है। 3x^3 - 2x + 5 जैसा कुछ लिखें।
नतीजा
मान डालें और नतीजा देखने के लिए “गणना करें” दबाएँ।
सूत्र
The power rule: bring the power down and reduce it by one.
यह कैलकुलेटर कैसे इस्तेमाल करें
- Type the polynomial. Implicit multiplication like 3x or 2(x+1) works.
- Press Calculate.
हल किए गए उदाहरण
Differentiate 3x³ − 2x + 5
3x³ → 9x², −2x → −2, and the constant 5 → 0.
So f′(x) = 9x² − 2 and f″(x) = 18x.
Medium: x⁴ − 3x² + 7
Power rule term by term: x⁴ → 4x³, −3x² → −6x, and the constant 7 → 0.
f′(x) = 4x³ − 6x. Differentiating again: f″(x) = 12x² − 6.
Hard: a power of a bracket, (2x + 1)³
Expand first: (2x + 1)³ = 8x³ + 12x² + 6x + 1.
Differentiate: f′(x) = 24x² + 24x + 6. The chain rule gives the same: 3(2x + 1)² × 2 = 6(4x² + 4x + 1).
f″(x) = 48x + 24.
आम गलतियाँ
- Forgetting to multiply by the old power: the derivative of x⁴ is 4x³, not x³.
- Keeping the constant: the derivative of a constant such as 7 is 0.
- Differentiating (2x + 1)³ as 3(2x + 1)² without the chain-rule factor 2.
अक्सर पूछे जाने वाले सवाल
What does a differentiate calculator do?
It finds the derivative — the rate of change, or the slope of the tangent — of a function. For polynomials this is the power rule applied to every term.
Which functions are supported?
Polynomials (powers of one variable). For sin, eˣ or ln, use Sumzo AI.
What is the second derivative?
The derivative of the derivative — it describes how the slope itself changes (concavity).