What is the derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} ?

The derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} is (-32-63x^{17/12}+60x^{7/3})/(12x^{5/3)}

What is the first derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} ?

The first derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} is (-32-63x^{17/12}+60x^{7/3})/(12x^{5/3)}

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\frac{d}{d x} (3 x^{\frac{5}{3}} + 4 x^{- \frac{2}{3}} - 7 x^{\frac{3}{4}})

\frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}

Solution steps

\frac{d}{d x} (3 x^{\frac{5}{3}} + 4 x^{- \frac{2}{3}} - 7 x^{\frac{3}{4}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{\frac{5}{3}}) + \frac{d}{d x} (4 x^{- \frac{2}{3}}) - \frac{d}{d x} (7 x^{\frac{3}{4}})

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

\frac{d}{d x} (4 x^{- \frac{2}{3}}) = - \frac{8}{3 x ^{\frac{5}{3}}}

\frac{d}{d x} (7 x^{\frac{3}{4}}) = \frac{21}{4 x ^{\frac{1}{4}}}

= 5 x^{\frac{2}{3}} - \frac{8}{3 x ^{\frac{5}{3}}} - \frac{21}{4 x ^{\frac{1}{4}}}

Simplify

5 x^{\frac{2}{3}} - \frac{8}{3 x ^{\frac{5}{3}}} - \frac{21}{4 x ^{\frac{1}{4}}} : \frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}

= \frac{- 32 - 63 x ^{\frac{17}{12}} + 60 x ^{\frac{7}{3}}}{12 x ^{\frac{5}{3}}}

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What is the derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} ?
The derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} is (-32-63x^{17/12}+60x^{7/3})/(12x^{5/3)}
What is the first derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} ?
The first derivative of 3x^{5/3}+4x^{-2/3}-7x^{3/4} is (-32-63x^{17/12}+60x^{7/3})/(12x^{5/3)}