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Derivative - Wikipedia

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The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable.[1] The process of finding a derivative is called differentiation. There are multiple different notations for differentiation, two of the most commonly used being Leibniz notation and prime notation. Leibniz notation, named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas prime notation is written by adding a prime mark. Higher order notations represent repeated differe

Derivative - Wikipedia Jump to content From Wikipedia, the free encyclopedia Instantaneous rate of change (mathematics) For other uses, see Derivative (disambiguation) . The graph of a function , drawn in black, and a tangent line to that graph, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point. The derivative at different points of a differentiable function. In this case, the derivative is equal to ⁠ sin ⁡ ( x 2 ) + 2 x 2 cos ⁡ ( x 2 ) {\displaystyle \sin \left(x^{2}\right)+2x^{2}\cos \left(x^{2}\right)} ⁠ . Part of a series of articles

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