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

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Answer 1 · 2018-03-31T16:30:38

$\frac{d y}{d x} = x^{2} e^{2 x} (3 + 2 x)$ $dy/dx = x^2e^{2x}(3+2x)$

$\frac{d}{d x} [u v] = \frac{d u}{d x} v + \frac{d v}{d x} u$ $d/dx[uv] = {du}/dx v + {dv}/dx u$

$u = x^{3}$ $u=x^3$
$v = e^{2 x}$ $v=e^{2x}$

$\frac{d y}{d x} = \frac{d}{d x} [x^{3}] e^{2 x} + \frac{d}{d x} [e^{2 x}] x^{3}$ $dy/dx = d/dx[x^3]e^{2x}+d/dx[e^{2x}]x^3$

$\frac{d y}{d x} = 3 x^{2} e^{2 x} + 2 e^{2 x} x^{3}$ $dy/dx = 3x^2e^{2x}+2e^{2x}x^3$

$\frac{d y}{d x} = x^{2} e^{2 x} (3 + 2 x)$ $dy/dx = x^2e^{2x}(3+2x)$

How do you find the derivative of f(x)= (x^3)(e^(2x))f(x)=(x3)(e2x)f(x)= (x^3)(e^(2x))?