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CBSE Class 12-science Answered

Find the second order derivative  of e3x sin 4x Explain in great detail  
Asked by haroonrashidgkp | 24 Aug, 2018, 11:12: PM
answered-by-expert Expert Answer
y = e3x sin 4x
begin mathsize 16px style dy over dx equals straight e to the power of 3 straight x end exponent straight d over dx sin 4 straight x plus sin 4 straight x fraction numerator begin display style straight d end style over denominator begin display style dx end style end fraction straight e to the power of 3 straight x end exponent fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals straight e to the power of 3 straight x end exponent open parentheses 4 cos 4 straight x close parentheses plus sin 4 straight x open parentheses 3 straight e to the power of 3 straight x end exponent close parentheses fraction numerator begin display style dy end style over denominator begin display style dx end style end fraction equals straight e to the power of 3 straight x end exponent open parentheses 4 cos 4 straight x plus 3 sin 4 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 straight e to the power of 3 straight x end exponent fraction numerator begin display style straight d end style over denominator begin display style dx end style end fraction open parentheses 4 cos 4 straight x plus 3 sin 4 straight x close parentheses plus open parentheses 4 cos 4 straight x plus 3 sin 4 straight x close parentheses fraction numerator begin display style straight d end style over denominator begin display style dx end style end fraction straight e to the power of 3 straight x end exponent fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals straight e to the power of 3 straight x end exponent open parentheses negative 16 sin 4 straight x plus 12 cos 4 straight x close parentheses plus open parentheses 4 cos 4 straight x plus 3 sin 4 straight x close parentheses 3 straight e to the power of 3 straight x end exponent fraction numerator begin display style straight d squared straight y end style over denominator begin display style dx squared end style end fraction equals straight e to the power of 3 straight x end exponent open parentheses negative 16 sin 4 straight x plus 12 cos 4 straight x plus 12 cos 4 straight x plus 9 sin 4 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 straight e to the power of 3 straight x end exponent open parentheses negative 7 sin 4 straight x plus 24 cos 4 straight x close parentheses end style
Answered by Sneha shidid | 27 Aug, 2018, 09:26: AM

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