This calculator is designed to help students and professionals compute derivatives of functions easily. By entering a function and specifying the variable, users can see immediate results, helping in understanding calculus concepts or solving mathematical problems.
All calculations are strictly based on standard mathematical formulas for derivatives. For further mathematical rigor, please refer to calculus textbooks and scholarly articles.
Power Rule: \( \frac{d}{dx} x^n = n \cdot x^{n-1} \)
Product Rule: \( \frac{d}{dx} (uv) = u'v + uv' \)
Chain Rule: \( \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x) \)
Consider the function \( f(x) = x^2 + 3x + 2 \). To find the derivative, apply the power rule to get \( f'(x) = 2x + 3 \).
A derivative represents the rate of change of a function with respect to a variable.
You can calculate a derivative by using rules of differentiation, such as the power rule, product rule, and chain rule.
Derivatives are fundamental in calculus for understanding changes, modeling real-world situations, and solving problems in science and engineering.
Our calculator is designed to handle a wide range of functions, but for highly complex expressions, manual verification is recommended.
The chain rule is a formula for computing the derivative of the composition of two or more functions.