Find dy/dx

 

y = xx . e(2x + 5)

 

 

mention each and every step

Asked by haroonrashidgkp | 11th Jul, 2018, 12:09: PM

Expert Answer:

y = xx e2x + 5 
Taking log on both sides
log y = log (xx e2x + 5)
begin mathsize 16px style log space straight y equals log space straight x to the power of straight x space plus space log space straight e to the power of 2 straight x plus 5 end exponent
log space straight y space equals xlog space straight x space plus space 2 straight x space plus space 5
1 over straight y dy over dx equals straight x cross times 1 over straight x plus log space straight x space plus space 2
fraction numerator begin display style 1 end style over denominator begin display style straight y end style end fraction fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals 1 plus log space straight x space plus space 2
fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals straight y open parentheses 3 plus log space straight x close parentheses
fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals open parentheses straight x to the power of straight x straight e to the power of 2 straight x plus 5 end exponent close parentheses open parentheses 3 plus log space straight x close parentheses end style

Answered by Sneha shidid | 11th Jul, 2018, 12:20: PM