What is the derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 ?

The derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 is (20x^{13/15}+63x^{7/10}-24)/(6x^{1/5)}-8

What is the first derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 ?

The first derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 is (20x^{13/15}+63x^{7/10}-24)/(6x^{1/5)}-8

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\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

\frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

Solution steps

\frac{d}{d x} (2 x^{\frac{5}{3}} - 5 x^{\frac{4}{5}} + 7 x^{\frac{3}{2}} - 8 x + 17)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{\frac{5}{3}}) - \frac{d}{d x} (5 x^{\frac{4}{5}}) + \frac{d}{d x} (7 x^{\frac{3}{2}}) - \frac{d}{d x} (8 x) + \frac{d}{d x} (17)

\frac{d}{d x} (2 x^{\frac{5}{3}}) = \frac{10 x ^{\frac{2}{3}}}{3}

\frac{d}{d x} (5 x^{\frac{4}{5}}) = \frac{4}{x ^{\frac{1}{5}}}

\frac{d}{d x} (7 x^{\frac{3}{2}}) = \frac{21 x ^{\frac{1}{2}}}{2}

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (17) = 0

= \frac{10 x ^{\frac{2}{3}}}{3} - \frac{4}{x ^{\frac{1}{5}}} + \frac{21 x ^{\frac{1}{2}}}{2} - 8 + 0

Simplify

\frac{10 x ^{\frac{2}{3}}}{3} - \frac{4}{x ^{\frac{1}{5}}} + \frac{21 x ^{\frac{1}{2}}}{2} - 8 + 0 : \frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

= \frac{20 x ^{\frac{13}{15}} + 63 x ^{\frac{7}{10}} - 24}{6 x ^{\frac{1}{5}}} - 8

What is the derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 ?
The derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 is (20x^{13/15}+63x^{7/10}-24)/(6x^{1/5)}-8
What is the first derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 ?
The first derivative of 2x^{5/3}-5x^{4/5}+7x^{3/2}-8x+17 is (20x^{13/15}+63x^{7/10}-24)/(6x^{1/5)}-8