Question

Find the second order derivatives of the following functions : e^{6 x} cos 3x

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Solution

Let space space space space space straight y equals straight e to the power of 6 straight x end exponent space cos space 3 straight x therefore space dy over dx equals 6 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 3 straight e to the power of 6 straight x end exponent space sin 3 straight x space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 36 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 18 straight e to the power of 6 straight x end exponent space sin 3 straight x minus 18 straight e to the power of 6 straight x end exponent sin space 3 straight x minus 9 straight e to the power of 6 straight x end exponent space cos 3 straight x space space space space space space space space space space space space space space equals 27 straight e to the power of 6 straight x end exponent space cos 3 straight x minus 36 straight e to the power of 6 straight x end exponent space sin 3 straight x equals 9 straight e to the power of 6 straight x end exponent space left parenthesis 3 cos space straight x minus 4 space sin space 3 straight x right parenthesis

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