What is the derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 ?

The derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 is (-1+4x^{4/3})/(4x^{2/3)}

What is the first derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 ?

The first derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 is (-1+4x^{4/3})/(4x^{2/3)}

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derivative of

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 6

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

Solution steps

\frac{d}{d x} (\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 6)

Simplify

\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{4} x^{\frac{1}{3}} + 6 : \frac{3 x ^{\frac{5}{3}}}{5} - \frac{3 x ^{\frac{1}{3}}}{4} + 6

= \frac{d}{d x} (\frac{3 x ^{\frac{5}{3}}}{5} - \frac{3 x ^{\frac{1}{3}}}{4} + 6)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{3 x ^{\frac{5}{3}}}{5}) - \frac{d}{d x} (\frac{3 x ^{\frac{1}{3}}}{4}) + \frac{d}{d x} (6)

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

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

\frac{d}{d x} (6) = 0

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

Simplify

x^{\frac{2}{3}} - \frac{1}{4 x ^{\frac{2}{3}}} + 0 : \frac{- 1 + 4 x ^{\frac{4}{3}}}{4 x ^{\frac{2}{3}}}

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

What is the derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 ?
The derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 is (-1+4x^{4/3})/(4x^{2/3)}
What is the first derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 ?
The first derivative of 3/5 x^{5/3}-3/4 x^{1/3}+6 is (-1+4x^{4/3})/(4x^{2/3)}