What is the derivative of 3x^4+2x^{1/3}-1/(x^2) ?

The derivative of 3x^4+2x^{1/3}-1/(x^2) is (2x^3+6x^{2/3}+36x^{20/3})/(3x^{11/3)}

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

The first derivative of 3x^4+2x^{1/3}-1/(x^2) is (2x^3+6x^{2/3}+36x^{20/3})/(3x^{11/3)}

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

\frac{2 x ^{3} + 6 x ^{\frac{2}{3}} + 36 x ^{\frac{20}{3}}}{3 x ^{\frac{11}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

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

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

= 12 x^{3} + \frac{2}{3 x ^{\frac{2}{3}}} - (- \frac{2}{x ^{3}})

Simplify

12 x^{3} + \frac{2}{3 x ^{\frac{2}{3}}} - (- \frac{2}{x ^{3}}) : \frac{2 x ^{3} + 6 x ^{\frac{2}{3}} + 36 x ^{\frac{20}{3}}}{3 x ^{\frac{11}{3}}}

= \frac{2 x ^{3} + 6 x ^{\frac{2}{3}} + 36 x ^{\frac{20}{3}}}{3 x ^{\frac{11}{3}}}

\int \frac{- 11 x - 24}{125 ( x ^{2} + 4 x + 5 )} d x

n = 1 \sum \infty \frac{2}{5 ^{n + 2}}

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

\int \frac{5 x}{2 - x ^{4}} d x

What is the derivative of 3x^4+2x^{1/3}-1/(x^2) ?
The derivative of 3x^4+2x^{1/3}-1/(x^2) is (2x^3+6x^{2/3}+36x^{20/3})/(3x^{11/3)}
What is the first derivative of 3x^4+2x^{1/3}-1/(x^2) ?
The first derivative of 3x^4+2x^{1/3}-1/(x^2) is (2x^3+6x^{2/3}+36x^{20/3})/(3x^{11/3)}