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Using Leibnitz’s Theorem find the nth derivative of y=(x^3)(e^4x)cos(3x)

Using Leibnitz’s Theorem find the nth derivative of y=(x^3)(e^4x)cos(3x)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
one way to do it is to write cos4x as (e^i4x + e^–i4x)/2.
then, the fn x^2 e^3x cos4x would turn into a form like:
1/2*(x^2 e^ax + x^2 e^bx) where a and b are constants obviously.
now, applying leibnitz theorem on fn of the form x^2*e^cx is very straight forward and easy.
kindly approve :)

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