# 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?
10. ### Hyperbolic trig identity for tanh (2x) using exponential definitions

Hey, Using exponential definitions, show that tanh(2x)= (2tanh(x))/(1+tanh^2(x)) Please help. Thanks
11. ### How do you derive the formula of S csch(x)(dx)=ln (tanh (x/2)) +C ?

The integrand can be transformed to functions of tanh (x/2) by first observing that sinh 2A = 2sinh A cosh A, from which csch(x) = 1/(2sinh(x/2)cosh(x/2)). Clever algebra, followed by an application of the Pythagorean properties, produces the desired result. Then substitute u for tanh(x/2)...
12. ### Hyperbolic Function (tanh & sech)

Q: Solve the equation 4 \mathrm{tanh}x - \mathrm{sech} x = 1 giving your solution in logarithmic form. __________________ My Method: 4 \mathrm{tanh}x - \mathrm{sech} x = 1 \therefore4 \left( \frac{e^x - e^{-x}}{e^x + e^{-x}} \right) - \left( \frac{2}{e^x + e^{-x}} \right) = 1 \therefore...
13. ### Differentiation of tanh?

Hi Im trying to differentiate w = (gktanh(hk))^0.5 dw/dk = ? Any help anyone? Many thanks in advance! zentus