What is the derivative of 1/3 x^{3/2}-x^{1/2} ?

The derivative of 1/3 x^{3/2}-x^{1/2} is (x^{1/2})/2-1/(2x^{1/2)}

What is the first derivative of 1/3 x^{3/2}-x^{1/2} ?

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

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

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d y}{d x} + 6 y = 9

\int_{0}^{5} x^{2} (x - 5)^{4} d x

x \to 2 lim (\frac{x - 2}{x ^{3} - 8})

f^{^{'}} (x) = x^{3} - 5 x^{2} + 3

256 = 4 x^{2} + 2 x y - 4 y^{3}, (2, - 4)

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