What is the derivative of-2/5 x^{5/2}+32x^{1/2} ?

The derivative of-2/5 x^{5/2}+32x^{1/2} is (16-x^2)/(x^{1/2)}

What is the first derivative of-2/5 x^{5/2}+32x^{1/2} ?

The first derivative of-2/5 x^{5/2}+32x^{1/2} is (16-x^2)/(x^{1/2)}

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\frac{d}{d x} (- \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}})

\frac{16 - x ^{2}}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (- \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}})

Simplify

- \frac{2}{5} x^{\frac{5}{2}} + 32 x^{\frac{1}{2}} : - \frac{2 x ^{\frac{5}{2}}}{5} + 32 x^{\frac{1}{2}}

= \frac{d}{d x} (- \frac{2 x ^{\frac{5}{2}}}{5} + 32 x^{\frac{1}{2}})

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (\frac{2 x ^{\frac{5}{2}}}{5}) + \frac{d}{d x} (32 x^{\frac{1}{2}})

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

\frac{d}{d x} (32 x^{\frac{1}{2}}) = \frac{16}{x ^{\frac{1}{2}}}

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

Simplify

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

= \frac{16 - x ^{2}}{x ^{\frac{1}{2}}}

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

\int x^{3} - 8 x^{2} + 16 x + 1 d x

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

\int e^{7 x + 1} d x

\frac{\partial}{\partial x} (\frac{x + 3}{y + 3})

What is the derivative of-2/5 x^{5/2}+32x^{1/2} ?
The derivative of-2/5 x^{5/2}+32x^{1/2} is (16-x^2)/(x^{1/2)}
What is the first derivative of-2/5 x^{5/2}+32x^{1/2} ?
The first derivative of-2/5 x^{5/2}+32x^{1/2} is (16-x^2)/(x^{1/2)}