What is the derivative of $(3x^3)/e^x$ ?

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Answer 1 · 2017-09-18T18:35:46

$9x^2e^-x -3x^3e^-x = (3x^2 (3-x))/e^x$

Note that $1/e^x = e^-x ->f (x) = 3x^3e^zx$ .

Now we can use the product rule. $f (x)=g (x)h (x) -> f'(x) = g'(x)h (x)+f (x)g'(x)$

The power rule and definition of the derivative of $e^u$ give us $d/ dx (3x^3) = 9x^2, d/dx (e^-x) = -e^-x$

Thus...

$f'(x) = 9x^2e^-x -3x^3e^-x = (3x^2 (3-x))/e^x$

What is the derivative of (3x^3)/e^x(3x^3)/e^x?