What is the derivative of (\sqrt[3]{x})/(x-9) ?

The derivative of (\sqrt[3]{x})/(x-9) is (x-9-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-9)^2}

What is the first derivative of (\sqrt[3]{x})/(x-9) ?

The first derivative of (\sqrt[3]{x})/(x-9) is (x-9-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-9)^2}

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derivative of

\frac{3 x}{x - 9}

\frac{x - 9 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ) ( x - 9 ) - \frac{d}{d x} ( x - 9 ) 3 x}{( x - 9 ) ^{2}}

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

\frac{d}{d x} (x - 9) = 1

= \frac{\frac{1}{3 x ^{\frac{2}{3}}} ( x - 9 ) - 1 \cdot 3 x}{( x - 9 ) ^{2}}

Simplify

\frac{\frac{1}{3 x ^{\frac{2}{3}}} ( x - 9 ) - 1 \cdot 3 x}{( x - 9 ) ^{2}} : \frac{x - 9 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 9 ) ^{2}}

= \frac{x - 9 - 3 3 x x ^{\frac{2}{3}}}{3 x ^{\frac{2}{3}} ( x - 9 ) ^{2}}

ln (3 x)

(x^{3} - 4 x)^{10}

\int \frac{1}{x ^{2} + 7 x + 12} d x

\int (sec (x) tan (x) - (sec (x))^{2}) d x

\frac{d}{d x} (\frac{[ 3 x ^{2} ]}{[ x ^{2} - 4 ]})

What is the derivative of (\sqrt[3]{x})/(x-9) ?
The derivative of (\sqrt[3]{x})/(x-9) is (x-9-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-9)^2}
What is the first derivative of (\sqrt[3]{x})/(x-9) ?
The first derivative of (\sqrt[3]{x})/(x-9) is (x-9-3\sqrt[3]{x}x^{2/3})/(3x^{2/3)(x-9)^2}