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Magazine Problem 383
\(\quad\) Prove $$ \sinh (x+y)=\sinh (x) \cosh (y)+\cosh (x) \sinh (y) $$ changing the expression to exponentials.
Problem 386
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ \text { [T] } \sinh \left(x^{2}\right) $$
Problem 387
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ \text { ITI } \frac{1}{\cosh (x)} $$
Problem 388
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ \text { IT] } \sinh (\ln (x)) $$
Problem 389
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ [\mathrm{T}] \cosh ^{2}(x)+\sinh ^{2}(x) $$
Problem 390
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ \text { [T] } \cosh ^{2}(x)-\sinh ^{2}(x) $$
Problem 391
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ [\mathrm{T}] \tanh \left(\sqrt{x^{2}+1}\right) $$
Problem 392
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ \text { [T] } \frac{1+\tanh (x)}{1-\tanh (x)} $$
Problem 393
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ [\mathrm{T}] \sinh ^{6}(x) $$
Problem 394
For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct. $$ [\mathrm{T}] \ln (\operatorname{sech}(x)+\tanh (x)] $$
