Derivative Calculator
Select a function type, enter coefficients, and get the derivative using the appropriate differentiation rule. Optionally evaluate the derivative at a specific x value.
Differentiation Rules
Frequently Asked Questions
A derivative measures the instantaneous rate of change of a function. Geometrically, it equals the slope of the tangent line to the function graph at a given point.
The Power Rule states that d/dx(xⁿ) = n·xⁿ⁻¹. For example, d/dx(x³) = 3x².
The Chain Rule is used to differentiate composite functions: d/dx[f(g(x))] = f′(g(x)) · g′(x). For example, d/dx[(2x+1)⁴] = 4(2x+1)³ · 2 = 8(2x+1)³.
d/dx(eˣ) = eˣ. More generally, d/dx(e^(bx)) = b·e^(bx). The exponential function is its own derivative, which is a unique property.
d/dx(ln(x)) = 1/x. More generally, d/dx(ln(bx)) = 1/x (the b cancels via chain rule). This is valid for x > 0.
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