# tanh

1. ### simple calculus question

Hi guys, I have a simple calculus question, (so simple it's actually embarrassing(Worried)) So I'm reading this article that says: \mbox{if we have: } p(D_i,D_i^* \mid \Psi) = \frac{1}{4w_i} sech^2(\frac{D_i^* - D_i}{2w_i}) \mbox{then: }\sum\limits_{i=1}^{N}log \frac{\int_{d_i}^{\infty}...
2. ### Imaginery Number with tanh

How do I solve this? Many thanks.
3. ### Power series for tanh?

Hi. How do I find the power series for tanh(z) (in the complex plane, if that matters, which it doesn't). I know the power series for sinh(z) and cosh(z) (same as sin(t), cos(t), but without the sign changes): \sinh(z)=\sum_{j=0}^\infty \frac{z^{2j+1}}{2j+1!} \cosh(z)=\sum_{j=0}^\infty...
4. ### Inverse tan and inverse of tanh

Hello, I know what the inverse of tan is when differentiated, but would the inverse of tanh differentiated follow the same format? -1/(1-x^2) Thank you!
5. ### Differentiation of inverse tanh

inverse tanh(X) = 1/2 ln(1+x/1-x) differentiate to show that d/dx = 1/1-x^2 I have been working on this problem for so long, can anyone show me the solution. Thanks!
6. ### tanh x properties

I'm having a few problems with the following questions: (i) differentiate tanh(x) and prove that it is a strictly increasing function. I've differentiated it to get sech^2(x) = 4/(e^x + e^-x)^2. Is it enough to say that since the differential is always positive, tanh(x) must then be...
7. ### tanh differentiable

tanh(x)= \frac{e^x- e^{-x}}{e^x+ e^{-x}} (a) Prove that tanh is differentiable. exp is differentiable, therefore tanh is differentiable?? The above has substraction and division by exp. How do i explain that tanh is still differentiable. (b) Prove that tanh is strictly increasing, and hence...
8. ### tanh

Can some one please me with the following question: Thank you in advance
9. ### limits for tanh

how do you do lim (x tanh (1/x)) as x tends to infinity? and lim (arctanh x / x) as x tends to 0? thanks. just wondering..when i am faced with limits questions involving hyperbolic functions, what are the steps that i should take?