Ad
related to: 2^x derivative proof table in excel
Search results
Results From The WOW.Com Content Network
Digamma function. In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: [ 1][ 2][ 3] It is the first of the polygamma functions. This function is strictly increasing and strictly concave on , [ 4] and it asymptotically behaves as [ 5] for complex numbers with large modulus ( ) in the sector with ...
In 1929, Carl Ludwig Siegel proved that J ν (x), J ' ν (x), and the logarithmic derivative J' ν (x) / J ν (x) are transcendental numbers when ν is rational and x is algebraic and nonzero. [51] The same proof also implies that K ν (x) is transcendental under the same assumptions. [52]
Definitions. For real non-zero values of x, the exponential integral Ei ( x) is defined as. The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero. For ...
The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4.The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1.
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. [ 1][ 2][ 3] Let , where both f and g are differentiable and The quotient rule states that the derivative of h(x) is. It is provable in many ways by using other derivative rules .
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1][ 2] In other words, is the probability that a normal (Gaussian) random variable will obtain a value larger than standard deviations. Equivalently, is the probability that a standard normal random variable takes a value larger than .
One proof of the chain rule begins by defining the derivative of the composite function f ∘ g, where we take the limit of the difference quotient for f ∘ g as x approaches a: ′ = (()) (()). Assume for the moment that g ( x ) {\displaystyle g(x)\!} does not equal g ( a ) {\displaystyle g(a)} for any x {\displaystyle x} near a ...
The derivative of the function at a point is the slope of the line tangent to the curve at the point. Slope of the constant function is zero, because the tangent line to the constant function is horizontal and its angle is zero. In other words, the value of the constant function, y, will not change as the value of x increases or decreases.
Ad
related to: 2^x derivative proof table in excel