Iwasawa power seriesp-adic measureEqui-distributionFerrero–Washington's theoremWe extend the result of Anglès (2007) [1], namely f ′ ( T ; θ ) ≢ 0 ( mod p ) for the Iwasawa power series f ( T ; θ ) ∈ Z ¯ p 〚 T − 1 〛 . For the derivative D = T d ...
Derivative f’ of function f(x)=arcsin x is: f’(x) = 1 / √(1 - x²) for all x in ]-1,1[. To show this result, we use derivative of the inverse function sin x. Derivative of arcsin x Derivative $f’$ of function $f(x)=\arcsin{x}$ is: \(\forall x \in ]–1, ...
Derivative $f’$ of the function $f(x)=\tan x$ is: \(\forall x \neq \frac{\pi}{2}+k\pi, k \in \mathbb{Z}, f'(x) = 1+\tan ^{2} x\) Proof First we have: \((\tan x)' =\lim _{h \rightarrow 0} \dfrac{\tan (x+h) - \tan x }{h}\) Now, let’s simplif...
Derivative f’ of the function f(x)=sinx is: f’(x) = cos x for any value of x. Derivative of sin x Derivative $f’$ of the function $f(x)=\sin x$ is: \(\forall x \in ]-\infty, +\infty[ , f'(x) = \cos x\) Proof/Demonstration \[\begin{aligned} \frac{\sin (x+...
Derivatives of functions table Function nameFunctionDerivative f(x) f'(x) Constant const 0 Linear x 1 Power xa a xa-1 Exponential ex ex Exponential ax axlna Natural logarithm ln(x) Logarithm logb(x) Sine sinx cosx Cosine cosx -sinx ...
(In other words the derivative of x3 is 3x2)So it is simply this:"multiply by power then reduce power by 1"It can also be used in cases like this:Example: What is ddx(1/x) ? 1/x is also x-1 We can use the Power Rule, where n = −1: ddxxn = nxn−1 ddxx−1 =...
The derivative of a constant function is one of the most basic and straightforward differentiation rules that students must know. It is a rule of differentiation derived from the power rule that serves as a shortcut to finding the derivative of any constant function and bypassing solving limits....
X(m)=∑k=−LLb[k]e−j2πmk/N=12LTse−j2πm(−L)/N−12LTse−j2πmL/NX(m)=e−j2πm(−L)/N−e−j2πnL/N2LTs=−jsin(2πmL/N)LTswhere L is the skip factor and N is the number of samples in the waveform. To put this equation in terms of frequency,...
Derivative Proof of sin(x) We can prove the derivative of sin(x) using the limit definition and the double angle formula for trigonometric functions.
In this paper we study the evolution of a flat Friedmann-Robertson-Walker model filled with a perfect fluid and a scalar field minimally coupled to gravity in higher derivative theory of gravitation. Exact solution of the field equations are obtained by the assumption of power-law form of the ...