What is the derivative of 8x^{2/3}+x^{5/3} ?

The derivative of 8x^{2/3}+x^{5/3} is (16+5x)/(3x^{1/3)}

What is the first derivative of 8x^{2/3}+x^{5/3} ?

The first derivative of 8x^{2/3}+x^{5/3} is (16+5x)/(3x^{1/3)}

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\frac{d}{d x} (8 x^{\frac{2}{3}} + x^{\frac{5}{3}})

\frac{16 + 5 x}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (8 x^{\frac{2}{3}} + x^{\frac{5}{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (8 x^{\frac{2}{3}}) + \frac{d}{d x} (x^{\frac{5}{3}})

\frac{d}{d x} (8 x^{\frac{2}{3}}) = \frac{16}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (x^{\frac{5}{3}}) = \frac{5 x ^{\frac{2}{3}}}{3}

= \frac{16}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3}

Simplify

\frac{16}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3} : \frac{16 + 5 x}{3 x ^{\frac{1}{3}}}

= \frac{16 + 5 x}{3 x ^{\frac{1}{3}}}

x \to - 4 lim (\frac{1}{4} + \frac{1}{x})

\frac{d}{d x} ((cos (6 x))^{x})

x \to 0 lim (x^{3} ln (x))

x \to 0 lim (\frac{1 - 6 x}{x})

\int \frac{x}{( x + 1 )} d x

What is the derivative of 8x^{2/3}+x^{5/3} ?
The derivative of 8x^{2/3}+x^{5/3} is (16+5x)/(3x^{1/3)}
What is the first derivative of 8x^{2/3}+x^{5/3} ?
The first derivative of 8x^{2/3}+x^{5/3} is (16+5x)/(3x^{1/3)}