What is the derivative of 4x^{2/3}+x^{5/3} ?

The derivative of 4x^{2/3}+x^{5/3} is (8+5x)/(3x^{1/3)}

What is the first derivative of 4x^{2/3}+x^{5/3} ?

The first derivative of 4x^{2/3}+x^{5/3} is (8+5x)/(3x^{1/3)}

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\frac{d}{d x} (4 x^{\frac{2}{3}} + x^{\frac{5}{3}})

\frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (4 x^{\frac{2}{3}} + x^{\frac{5}{3}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x^{\frac{2}{3}}) + \frac{d}{d x} (x^{\frac{5}{3}})

\frac{d}{d x} (4 x^{\frac{2}{3}}) = \frac{8}{3 x ^{\frac{1}{3}}}

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

= \frac{8}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3}

Simplify

\frac{8}{3 x ^{\frac{1}{3}}} + \frac{5 x ^{\frac{2}{3}}}{3} : \frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

= \frac{8 + 5 x}{3 x ^{\frac{1}{3}}}

f (x) = x^{3} - 2 x, at x = 2

\frac{d y}{d x} + 5 (tan (5 x)) y = 3 cos (5 x)

\int 60 x^{2} (1 - 4 x^{3})^{4} d x

f (x) = x^{\frac{5}{6}}

What is the derivative of 4x^{2/3}+x^{5/3} ?
The derivative of 4x^{2/3}+x^{5/3} is (8+5x)/(3x^{1/3)}
What is the first derivative of 4x^{2/3}+x^{5/3} ?
The first derivative of 4x^{2/3}+x^{5/3} is (8+5x)/(3x^{1/3)}