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CBSE Class 12-science Answered

Find the second order derivative of  sin 3x cos 5x  
Asked by haroonrashidgkp | 24 Aug, 2018, 11:12: PM
answered-by-expert Expert Answer
y = sin3x cos5x
begin mathsize 16px style dy over dx equals sin 3 straight x straight d over dx cos 5 straight x plus cos 5 straight x fraction numerator begin display style straight d end style over denominator begin display style dx end style end fraction sin 3 straight x fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals sin 3 straight x open parentheses negative 5 sin 5 straight x close parentheses plus cos 5 straight x open parentheses 3 cos 3 straight x close parentheses fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals negative 5 sin 3 xsin 5 straight x plus 3 cos 5 xcos 3 straight x fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals negative 5 sin 3 straight x open parentheses 5 cos 5 straight x close parentheses plus sin 5 straight x open parentheses negative 15 cos 3 straight x close parentheses plus 3 cos 5 straight x open parentheses negative 3 sin 3 straight x close parentheses plus cos 3 straight x open parentheses negative 15 sin 5 straight x close parentheses fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals negative 25 sin 3 xcos 5 straight x minus 15 sin 5 xcos 3 straight x minus 9 sin 3 xcos 5 straight x minus 15 sin 5 xcos 3 straight x fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals open parentheses negative 25 sin 3 xcos 5 straight x minus 9 sin 3 xcos 5 straight x close parentheses minus 15 sin 5 xcos 3 straight x minus 15 sin 5 xcos 3 straight x fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals negative 34 sin 3 xcos 5 straight x minus 30 sin 5 xcos 3 straight x end style
Answered by Sneha shidid | 27 Aug, 2018, 09:10: AM

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