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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 ...
Intuitive (geometric) explanation. Differentiation is linear. The product rule. The chain rule. The inverse function rule. Power laws, polynomials, quotients, and reciprocals. The polynomial or elementary power rule. The reciprocal rule. The quotient rule.
In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely, if is the function such that for every x, then the chain rule is, in Lagrange's notation , or, equivalently,
The higher order partial derivatives can be obtained by successive differentiation Antiderivative analogue. There is a concept for partial derivatives that is analogous to antiderivatives for regular derivatives. Given a partial derivative, it allows for the partial recovery of the original function. Consider the example of
Numerical differentiation. Finite difference estimation of derivative. In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
Calculus. In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. [1] It is one of the two traditional divisions of calculus, the other being integral calculus —the study of the area beneath a curve. [2]
Calculus. In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, [1] The technique is often performed in cases where it is easier to differentiate the logarithm of a function rather than the function itself.
f ′ ( x) A function f of x, differentiated once in Lagrange's notation. One of the most common modern notations for differentiation is named after Joseph Louis Lagrange, even though it was actually invented by Euler and just popularized by the former. In Lagrange's notation, a prime mark denotes a derivative.
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