"Find the fifth derivative of the function y=(x3+2x2+3x)ex." was answered by our community

CheemnCatelvew

Answered question

2021-05-17

Find the fifth derivative of the function

y = (x^{3} + 2 x^{2} + 3 x) e^{x}

AGRFTr

Skilled2021-05-18Added 95 answers

Step 1
We use the product rule to find the first two derivatives

y = (x^{3} + 2 x^{2} + 3 x) e^{x}

y^{(1)} = (3 x^{2} + 4 x + 3) e^{x} + (x^{3} + 2 x^{2} + 3 x) e^{x} = (x^{3} + 5 x^{2} + 7 x + 3) e^{x}

y^{(2)} = (3 x^{2} + 10 x + 7) e^{x} + (x^{3} + 5 x^{2} + 7 x + 3) e^{x} = (x^{3} + 8 x^{2} + 17 x + 10) e^{x}

Step 2
Use the product rule to find the other derivatives too.

y^{(2)} = (3 x^{2} + 10 x + 7) e^{x} + (x^{3} + 5 x^{2} + 7 x + 3) e^{x} = (x^{3} + 8 x^{2} + 17 x + 10) e^{x}

y^{(3)} = (3 x^{2} + 16 x + 17) e^{x} + (x^{3} + 8 x^{2} + 17 x + 10) e^{x} = (x^{3} + 11 x^{2} + 33 x + 27) e^{x}

y^{(4)} = (3 x^{2} + 22 x + 33) e^{x} + (x^{3} + 11 x^{2} + 33 x + 27) e^{x} = (x^{3} + 14 x^{2} + 55 x + 60) e^{x}

y^{(5)} = (3 x^{2} + 28 x + 55) e^{x} + (x^{3} + 14 x^{2} + 55 x + 60) e^{x} = (x^{3} + 17 x^{2} + 83 x + 115) e^{x}

Answer:

Jeffrey JordonExpert2021-12-25Added 2605 answers

Answer is given below (on video)

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