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In calculus, the power rule is used to differentiate functions of the form () =, whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule.
The most general power rule is the functional power rule: for any functions f and g, ... Differentiable function – Mathematical function whose derivative exists;
The derivative of a function at a chosen input value describes the rate of change of the function near that input value. ... This is known as the power rule.
Suppose that a function represents the position of an object at the time. The first derivative of that function is the velocity of an object with respect to time, the second derivative of the function is the acceleration of an object with respect to time, [29] and the third derivative is the jerk. [36]
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula ′ where ′ is the derivative of f. [1] Intuitively, this is the infinitesimal relative change in f ; that is, the infinitesimal absolute change in f, namely f ′ , {\displaystyle f',} scaled by the current ...
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()
The rule holds in that case because the derivative of a constant function is 0. If the rule holds for any particular exponent n, then for the next value, n + 1, we have + = = + = + = (+). Therefore, if the proposition is true for n, it is true also for n + 1, and therefore for all natural n.
In calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f. The reciprocal rule can be used to show that the power rule holds for negative exponents if it has already been established for positive exponents. Also, one can readily deduce the quotient rule from the reciprocal rule and ...