The Derivative Calculator finds the derivative of any mathematical function with respect to a chosen variable. It supports polynomials, trigonometric functions, exponentials, logarithms, and their compositions.
Enter your function and variable, then choose the order of differentiation. The calculator uses symbolic differentiation to provide exact results displayed in standard mathematical notation.
Your calculations will appear here
The derivative of a function measures its instantaneous rate of change at any point. Geometrically, the derivative at a point gives the slope of the tangent line to the function's graph at that point.
Key derivative rules include: the power rule d/dx(x^n) = n*x^(n-1), the product rule d/dx(fg) = f'g + fg', the chain rule d/dx(f(g(x))) = f'(g(x)) * g'(x), and the quotient rule.
Aufgabe: Find the derivative of f(x) = 3x^4
Loesung: Using the power rule: d/dx(3x^4) = 3 * 4 * x^3
Antwort: f'(x) = 12x^3
Aufgabe: Find the derivative of f(x) = sin(x) * cos(x)
Loesung: Using the product rule: cos(x)*cos(x) + sin(x)*(-sin(x)) = cos^2(x) - sin^2(x)
Antwort: f'(x) = cos(2x)
Aufgabe: Find the derivative of f(x) = (2x + 1)^5
Loesung: Outer: 5*(2x+1)^4, inner derivative: 2. Multiply: 5*2*(2x+1)^4
Antwort: f'(x) = 10(2x + 1)^4
Aufgabe: Find the second derivative of f(x) = x^3 - 6x
Loesung: f'(x) = 3x^2 - 6. f''(x) = 6x
Antwort: f''(x) = 6x
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