156 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



d tanh x d tann" 1 x d coth" 1 x i 



i -x 2 



dx 



I 



7.32 



i. 



dx 



du 



dv 



-r- 



dx 



V 2 



3> dx ~ ^ dx 



a. 



dyi i dyz 

 dx V* dx 



de u 

 [ ' te 



dx 



df(u) _ df(u) ^du 

 *' dx du dx 



7.33 Derivative of a Definite Integral. 



3. 



7.35 Higher Derivatives. 



