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

The derivative of (2x/(\sqrt[3]{x-2)}) is (2(3\sqrt[3]{x-2}(x-2)^{2/3}-x))/(3(x-2)^{4/3)}

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

The first derivative of (2x/(\sqrt[3]{x-2)}) is (2(3\sqrt[3]{x-2}(x-2)^{2/3}-x))/(3(x-2)^{4/3)}

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\frac{d}{d x} (\frac{2 x}{3 x - 2})

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

Solution steps

\frac{d}{d x} (\frac{2 x}{3 x - 2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

2 \cdot \frac{1 \cdot 3 x - 2 - \frac{1}{3 ( x - 2 ) ^{\frac{2}{3}}} x}{( 3 x - 2 ) ^{2}} : \frac{2 ( 3 3 x - 2 ( x - 2 ) ^{\frac{2}{3}} - x )}{3 ( x - 2 ) ^{\frac{4}{3}}}

= \frac{2 ( 3 3 x - 2 ( x - 2 ) ^{\frac{2}{3}} - x )}{3 ( x - 2 ) ^{\frac{4}{3}}}

\int x (x + 1) d x

\frac{d y}{d x}, e^{\frac{x}{y}} = x - y

y^{^{''}} + 16.67 y^{^{'}} + 10000 y = 0

y = 6 x^{2} - 6 x + 3, (1, 3)

\int 9 y d y

What is the derivative of (2x/(\sqrt[3]{x-2)}) ?
The derivative of (2x/(\sqrt[3]{x-2)}) is (2(3\sqrt[3]{x-2}(x-2)^{2/3}-x))/(3(x-2)^{4/3)}
What is the first derivative of (2x/(\sqrt[3]{x-2)}) ?
The first derivative of (2x/(\sqrt[3]{x-2)}) is (2(3\sqrt[3]{x-2}(x-2)^{2/3}-x))/(3(x-2)^{4/3)}