differentiate using logarithmic differentiation
 
 1. squareroot of (x+1)(x+2)(x+3)
                3       6         
 2.sin3x .(sinx)   .(cosx).cos6x
 
 
3 tanx .tan2x.tan3x.tan4x
                  x         3x
4 .squareroot of 2 .sin4x.e
                --------------
 
                 x+1    
 
                logx......infinity
           logx
 
5. y=logx 
 

Asked by Rajeev | 19th Jul, 2015, 06:37: PM

Expert Answer:

2. space f left parenthesis x right parenthesis equals sin 3 x space sin x space cos x space cos 6 x log f left parenthesis x right parenthesis equals log open square brackets s i n 3 x space s i n x space c o s x space c o s 6 x close square brackets D i f f e r e n t i a t i n g space b o t h space s i d e s space w i t h space r e s p e c t space t o space apostrophe x apostrophe space w e space g e t fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction f apostrophe left parenthesis x right parenthesis equals fraction numerator d over denominator d x end fraction open square brackets log sin 3 x space plus space log sin x space plus space log cos x space plus space log cos 6 x close square brackets rightwards double arrow fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction f apostrophe left parenthesis x right parenthesis equals fraction numerator 3 cos 3 x over denominator sin 3 x end fraction plus fraction numerator cos x over denominator sin x end fraction plus fraction numerator negative sin x over denominator cos x end fraction plus fraction numerator negative 6 sin 6 x over denominator cos 6 x end fraction rightwards double arrow f apostrophe left parenthesis x right parenthesis equals open parentheses s i n 3 x space s i n x space c o s x space c o s 6 x close parentheses open square brackets fraction numerator 3 c o s 3 x over denominator s i n 3 x end fraction plus fraction numerator c o s x over denominator s i n x end fraction minus fraction numerator s i n x over denominator c o s x end fraction minus fraction numerator 6 s i n 6 x over denominator c o s 6 x end fraction close square brackets

Answered by satyajit samal | 20th Jul, 2015, 09:06: AM