How do you find the derivative of $f (x) = 2 x^{3} e^{9 x}$ $f(x) = 2x^3 e^(9x)$ ?

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Answer 1 · 2015-05-17T00:19:08

The answer is : $f'(x) = 6e^(9x)x^2(1+3x)$

$f(x) = 2x^3e^(9x) = h(x)g(x)$ , where $h(x) = 2x^3$ and $g(x) = e^(9x)$ .

We will find the derivative with the product rule :

$f'(x) = h'(x)g(x) + h(x)g'(x) = (2x^3)'e^(9x)+2x^3(e^(9x))'$

$f'(x) = 2*3x^2*e^(9x) + 2x^3*9e^(9x) = 6x^2e^(9x) +18x^3e^(9x)$

$f'(x) = 6e^(9x)(x^2 + 3x^3) = 6e^(9x)x^2(1+3x)$

How do you find the derivative of f(x) = 2x^3 e^(9x)f(x)=2x3e9xf(x) = 2x^3 e^(9x)?