Как да изчислим Derivative
Какво е Derivative?
A derivative measures the instantaneous rate of change of a function — the slope of the tangent line at any point. Derivatives are the foundation of differential calculus and are used in physics (velocity, acceleration), economics (marginal cost), and optimisation.
Формула
Ръководство стъпка по стъпка
- 1Power rule: d/dx[xⁿ] = n·xⁿ⁻¹
- 2Chain rule: d/dx[f(g(x))] = f'(g(x)) · g'(x)
- 3Product rule: d/dx[f·g] = f'g + fg'
- 4Common derivatives: d/dx[sin x] = cos x, d/dx[eˣ] = eˣ, d/dx[ln x] = 1/x
Worked Examples
Frequently Asked Questions
What is Derivative Calc?
A derivative measures the instantaneous rate of change of a function — the slope of the tangent line at any point. Derivatives are the foundation of differential calculus and are used in physics (velocity, acceleration), economics (marginal cost), and optimisation
How accurate is the Derivative Calc calculator?
The calculator uses the standard published formula for derivative calc. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.
What units does the Derivative Calc calculator use?
This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.
What formula does the Derivative Calc calculator use?
The core formula is: Power rule: d/dx[xⁿ] = n·xⁿ⁻¹. Each step in the calculation is shown so you can verify the result manually.
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