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Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutor. Proof lnexy = xy = lnex lney = ln(ex ·ey) Since lnx is onetoone, then exy = ex ·ey 1 = e0 = ex(−x) = ex ·e−x ⇒ e−x = 1 ex ex−y = ex(−y) = ex ·e−y = ex · 1 ey ex ey • For r = m ∈ N, emx = e z }m { x···x = z }m { ex ···ex = (ex)m • For r = 1 n, n ∈ N and n 6= 0, ex = e n n x = e 1 nx n ⇒ e n x = (ex) 1 • For r rational, let r = m n, m, n ∈ N. ` o N ¢ æ q M Ï º q Ð s w ç 0 v è ` Ï ¬ Æ Q = ^ d b Ð U ¦ ó o M t 9 !.

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First, recall that (d/dt) t^t = t^t (1 ln t) via logarithmic differentiation Let y = t^t ==> ln y = t ln t Differentiate both sides (1/y) dy/dt = 1 ln t ==> dy/dt = y(1 ln t) = t^t (1 ln t)Remembering that z is a function of x, differentiate both sides with respect to x. ¥ A t t e m p t s o f c o n t in u a t io n s a t n o n in t e g e r b D le a d t o n u m e r ic a l in s t a b ilit ie s ( Y u z h i Ò L o u is Ó L iu Õs t a lk ) ¥ T h e d is c r e t e s c a lin g a llo w s ( s m a ll, o r d e r 1 0!. C x g e F T ؗj26 F40 ` e r ɂčD ̃A j V u X s h O t @ v7 27 DVD 1 ɐ 삯.

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