What is the derivative of \sqrt[3]{x}-7/(x^3+e^2) ?

The derivative of \sqrt[3]{x}-7/(x^3+e^2) is (x^4+63x^{2/3})/(3x^{14/3)}

What is the first derivative of \sqrt[3]{x}-7/(x^3+e^2) ?

The first derivative of \sqrt[3]{x}-7/(x^3+e^2) is (x^4+63x^{2/3})/(3x^{14/3)}

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\frac{x ^{4} + 63 x ^{\frac{2}{3}}}{3 x ^{\frac{14}{3}}}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d x} (\frac{7}{x ^{3}}) = - \frac{21}{x ^{4}}

\frac{d}{d x} (e^{2}) = 0

= \frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{21}{x ^{4}}) + 0

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{21}{x ^{4}}) + 0 : \frac{x ^{4} + 63 x ^{\frac{2}{3}}}{3 x ^{\frac{14}{3}}}

= \frac{x ^{4} + 63 x ^{\frac{2}{3}}}{3 x ^{\frac{14}{3}}}

\frac{d}{d x} (cot (x) + csc (x))

x \to 1 lim (\frac{1 - x ^{2}}{ln ( x )})

y^{^{'}} + \frac{4 y}{x} = - \frac{3}{x}

\frac{d}{d x} (2 e^{- 1.5 x} cos (3 x))

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

What is the derivative of \sqrt[3]{x}-7/(x^3+e^2) ?
The derivative of \sqrt[3]{x}-7/(x^3+e^2) is (x^4+63x^{2/3})/(3x^{14/3)}
What is the first derivative of \sqrt[3]{x}-7/(x^3+e^2) ?
The first derivative of \sqrt[3]{x}-7/(x^3+e^2) is (x^4+63x^{2/3})/(3x^{14/3)}