2016年11月2日 · dy/dx=1/(1-x^2) y=tanh^-1(1/x) => tanhy=1/x Differentiating implicitly gives: (1-tanh^2y)dy/dx=-1/x^2 :. (1-(1/x)^2)dy/dx=-1/x^2 :. dy/dx=-1/((x^2)(1-(1/x)^2)) :. dy ...

2015年4月16日 · Applying chain rule, the derivative would be 2e^(2x) sech^2 (1+e^(2x))

2018年4月19日 · The argument below can be adapted to prove that the inverse of any odd invertible function is odd. The function tanh(x) equiv (e^x-e^-x)/(e^x+e^-x) is obviously an odd …

2018年7月13日 · Find derivation of #tanh^-1x#, hence differentiate #y= tanh^-1 ((2x)/(1+x^2))# ? Calculus. 1 Answer

2017年7月24日 · I got = tanh(x)ln(tanh(x/2)) - 2arctan(tanh(x/2)) + C, " "x > 0 DISCLAIMER: VERY LONG ANSWER! Well, I don't work with hyperbolics much, but I do know that: the …

2017年5月17日 · The domain is x in RR the range is y in RR: 0 < y < pi The domain of the tanh(x) function is any real number: x in RR The range of the tanh(x) function is y in RR: -1 < y < 1; …

2018年6月2日 · 2192 views around the world You can reuse this answer ...

2018年5月30日 · = ln ((e^4 - 1)/(e^3 - e)) y=ln( (e^x-1)/(e^x+1)) =ln( tanh (x/2) ) Arc length: ds = sqrt(1 + (y')^2 ) dx (ln tanh (x/2))^' = 1/(tanh ( x/2)) sech^2 (x/2) * 1/2 =1/2 ...

2018年5月24日 · Given #y=f(x)#, #f'(x)=lim_(hto0)(f(x+h)-f(x))/h#. #f'(x)=lim_(hto0)(tanh(x+h)-tan(x))/h# #f'(x)=lim_(hto0)((tanh(x)+tanh(h))/(1+tanh(x)tanh(h))-tan(x))/h#

2017年9月27日 · As #tanh(x/2)=sqrt((coshx-1)/(coshx+1))# = #sqrt(((coshx-1)(coshx+1))/((coshx+1)(coshx+1))# = #sqrt(cosh^2x-1)/(coshx+1)#