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Continuity And Differentiability

Question
CBSEENMA12035335

Find the second order derivatives of the following functions : ex sin 5x

Solution
Let space straight y equals straight e to the power of straight x space sin space 5 straight x
space dy over dx equals straight e to the power of straight x space sin space 5 straight x plus 5 straight e to the power of straight x plus cos space 5 straight x
fraction numerator straight d squared straight y over denominator dx squared end fraction equals straight e to the power of straight x space sin space 5 straight x plus 5 straight e to the power of straight x space cos space 5 straight x plus 5 space straight e to the power of straight x space cos space 5 straight x minus 25 space straight e to the power of straight x space sin 5 straight x
space space space space space space space space space space equals 10 straight e to the power of straight x cos 5 minus 24 straight e to the power of straight x sin 5 straight x equals 2 straight e to the power of straight x left parenthesis 5 cos 5 straight x minus 12 sin 5 straight x right parenthesis

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