Question

derive a função
$x ^{3} + 2x - 8 \sqrt{ x}$
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Answer 1

$f(x)=x^3+2x-8\sqrt{x}\ \therefore\ \boxed{f(x)=x^3+2x-8x^{\frac{1}{2}}}$

$\dfrac{d}{dx}\big(f(x)\big)=\dfrac{d}{dx}\big(x^3+2x-8x^{\frac{1}{2}}\big)\ \therefore$

$\dfrac{d}{dx}\big(f(x)\big)=\dfrac{d}{dx}\big(x^3\big)+2\dfrac{d}{dx}\big(x\big)-8\dfrac{d}{dx}\big(x^{\frac{1}{2}}\big)\ \therefore$

$\dfrac{d}{dx}\big(f(x)\big)=3x^2+2-8\bigg(\dfrac{1}{2}x^{-\frac{1}{2}}\bigg)\ \therefore$

$\boxed{\dfrac{d}{dx}\big(f(x)\big)=3x^2+2-\dfrac{4}{\sqrt{x}}}$