What is the derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) ?

The derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) is (28x^{13/3}+6)/(3x^3)+2

What is the first derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) ?

The first derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) is (28x^{13/3}+6)/(3x^3)+2

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\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

\frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

Solution steps

\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 3 x^{7}) - \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (4 3 x^{7}) = \frac{28 x ^{\frac{4}{3}}}{3}

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

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

= \frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2

Simplify

\frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2 : \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

= \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

What is the derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) ?
The derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) is (28x^{13/3}+6)/(3x^3)+2
What is the first derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) ?
The first derivative of 4\sqrt[3]{x^7}-1/(x^2+2x) is (28x^{13/3}+6)/(3x^3)+2