Need to find derivative of $ y = \ln \operatorname{cosh}v - \frac 1 2 \operatorname{tanh}^2 v $
Any help would be appreciated. The answer is $ \operatorname{tanh}^3v $ but I have no clue how to get that.
I currently have $ \frac {1}{-\operatorname{sinh}v} - \frac 12 (2 \operatorname{tanh}v) * \operatorname{sech}^2v $ but I don't know how to get from there or if that's even correct.
So, you almost had it. But $$\frac{d}{dv}\left(\log \cosh (v)\right)=\tanh(v)$$ Therefore, we have
$$\begin{align} \frac{d}{dv}\left(\log \cosh (v)-\frac12 \tanh^2(v)\right)&=\tanh (v)-\tanh (v)\, \text{sech}^2 (v)\\\\ &=\tanh(v)(1-\text{sech}^2(v))\\\\ &=\tanh^3(v) \end{align}$$