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

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

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

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

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derivative of

Solution steps

Apply the Quotient Rule:

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

\frac{d}{d x} (x - 3) = 1

Simplify

\frac{\partial}{\partial x} (- x (2 x - y^{3}))

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

\int \frac{( x ^{2} )}{81 - x ^{2}} d x

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

(2, 6), (6, 6)

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