What is the derivative of (\sqrt[3]{x})/(x-6) ?

The derivative of (\sqrt[3]{x})/(x-6) is (x-6-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-6)^2}

What is the first derivative of (\sqrt[3]{x})/(x-6) ?

The first derivative of (\sqrt[3]{x})/(x-6) is (x-6-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-6)^2}

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derivative of

\frac{3 x}{x - 6}

\frac{x - 6 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{x - 6})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x ) ( x - 6 ) - \frac{d}{d x} ( x - 6 ) 3 x}{( x - 6 ) ^{2}}

\frac{d}{d x} (3 x) = \frac{1}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (x - 6) = 1

= \frac{\frac{1}{3 x ^{\frac{2}{3}}} ( x - 6 ) - 1 \cdot 3 x}{( x - 6 ) ^{2}}

Simplify

\frac{\frac{1}{3 x ^{\frac{2}{3}}} ( x - 6 ) - 1 \cdot 3 x}{( x - 6 ) ^{2}} : \frac{x - 6 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 6 ) ^{2}}

= \frac{x - 6 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 6 ) ^{2}}

f (x) = x^{2} e^{x} - 2 x e^{x} + 9 e^{x}

n = 8 \sum \infty \frac{1}{n ( n - 1 )}

\int_{0}^{1} (x^{2} - 4 x + 7) d x

\frac{d}{d x} (- 3 sin (x))

x \to 4 lim (\frac{x + 1}{x + 4})

What is the derivative of (\sqrt[3]{x})/(x-6) ?
The derivative of (\sqrt[3]{x})/(x-6) is (x-6-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-6)^2}
What is the first derivative of (\sqrt[3]{x})/(x-6) ?
The first derivative of (\sqrt[3]{x})/(x-6) is (x-6-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-6)^2}