Find the nth derivative of x² e^5x
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It can be explained as follows:
y = x^2e^5x
dy/dx = d(x^2e^5x)/dx
= x^2 d(e^5x) + e^5x d(x^2)
= x^2 e^5x + e^5x 2x
= e^5x(x^2 + 2x)
Let x be n,
So the nth derivative would be:
= e^5n(n^2 + 2n)
y = x^2e^5x
dy/dx = d(x^2e^5x)/dx
= x^2 d(e^5x) + e^5x d(x^2)
= x^2 e^5x + e^5x 2x
= e^5x(x^2 + 2x)
Let x be n,
So the nth derivative would be:
= e^5n(n^2 + 2n)
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