What is the derivative of (10\sqrt[3]{z})/(z^2) ?

The derivative of (10\sqrt[3]{z})/(z^2) is -(50)/(3z^{8/3)}

What is the first derivative of (10\sqrt[3]{z})/(z^2) ?

The first derivative of (10\sqrt[3]{z})/(z^2) is -(50)/(3z^{8/3)}

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derivative of

\frac{10 3 z}{z ^{2}}

- \frac{50}{3 z ^{\frac{8}{3}}}

Solution steps

\frac{d}{d z} (\frac{10 3 z}{z ^{2}})

Take the constant out:

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

= 10 \frac{d}{d z} (\frac{3 z}{z ^{2}})

Apply the Quotient Rule:

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

= 10 \cdot \frac{\frac{d}{d z} ( 3 z ) z ^{2} - \frac{d}{d z} ( z ^{2} ) 3 z}{( z ^{2} ) ^{2}}

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

\frac{d}{d z} (z^{2}) = 2 z

= 10 \cdot \frac{\frac{1}{3 z ^{\frac{2}{3}}} z ^{2} - 2 z 3 z}{( z ^{2} ) ^{2}}

Simplify

10 \cdot \frac{\frac{1}{3 z ^{\frac{2}{3}}} z ^{2} - 2 z 3 z}{( z ^{2} ) ^{2}} : - \frac{50}{3 z ^{\frac{8}{3}}}

= - \frac{50}{3 z ^{\frac{8}{3}}}

\frac{d}{d x} (A e^{3 x} \cdot 3)

\frac{s - 3}{s ^{2} + 4 s + 13}

\frac{[ y - y ^{2} ]}{t} = y^{^{'}}, y (1) = 2

x \to 0 lim (x (11 + \frac{4}{x}))

\int cos (\frac{nπ}{2} x) d x

What is the derivative of (10\sqrt[3]{z})/(z^2) ?
The derivative of (10\sqrt[3]{z})/(z^2) is -(50)/(3z^{8/3)}
What is the first derivative of (10\sqrt[3]{z})/(z^2) ?
The first derivative of (10\sqrt[3]{z})/(z^2) is -(50)/(3z^{8/3)}