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

The derivative of sqrt(x^3)+\sqrt[3]{x^2} is (9x^{5/6}+4)/(6\sqrt[3]{x)}

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

The first derivative of sqrt(x^3)+\sqrt[3]{x^2} is (9x^{5/6}+4)/(6\sqrt[3]{x)}

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

\frac{9 x ^{\frac{5}{6}} + 4}{6 3 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= \frac{3 x}{2} + \frac{2}{3 x ^{\frac{1}{3}}}

Simplify

\frac{3 x}{2} + \frac{2}{3 x ^{\frac{1}{3}}} : \frac{9 x ^{\frac{5}{6}} + 4}{6 3 x}

= \frac{9 x ^{\frac{5}{6}} + 4}{6 3 x}

\frac{d}{d x} (24 cos (3 x))

- 3 sin (3 x)

\frac{d}{d t} (8 t^{\frac{3}{2}})

y^{^{''}} + 4 y = csc (2 x)

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{( e ^{2 x} )}{x ^{2}}

What is the derivative of sqrt(x^3)+\sqrt[3]{x^2} ?
The derivative of sqrt(x^3)+\sqrt[3]{x^2} is (9x^{5/6}+4)/(6\sqrt[3]{x)}
What is the first derivative of sqrt(x^3)+\sqrt[3]{x^2} ?
The first derivative of sqrt(x^3)+\sqrt[3]{x^2} is (9x^{5/6}+4)/(6\sqrt[3]{x)}