Symbolic derivative calculator with step-by-step rules: power, product, quotient and chain rule.
A derivative calculator computes the symbolic derivative of any algebraic, trigonometric, exponential, or logarithmic function with respect to a chosen variable. Derivatives describe the instantaneous rate of change of a function — slope, velocity, marginal cost, or any "rate at a moment in time."
The result is given in simplified symbolic form, useful for both verifying hand-derived answers and for further analytical work (e.g. finding stationary points by setting f'(x) = 0).
\frac{df}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
Inputs: Differentiate f(x) = 3x² sin(x)
Velocity is the derivative of position with respect to time. Acceleration is the derivative of velocity. In economics, marginal cost is the derivative of total cost. Any time you ask "how fast is X changing?" you are asking for a derivative. The derivative is the slope of the tangent line to the function's graph at a point.
A function fails to be differentiable at a point if it has a sharp corner (e.g. |x| at x = 0), a vertical tangent (e.g. ∛x at x = 0), or a discontinuity. Differentiability is strictly stronger than continuity: continuous functions can fail to be differentiable, but every differentiable function is continuous.
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