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

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

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

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

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

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

Solution steps

\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}}}

d er i v a t i v e \frac{7}{r ^{3}}

d er i v a t i v e f (t) = 8 t sin (π t)

\frac{d}{d x} (x^{2 n})

\frac{d}{d x} (\frac{1}{9 - x ^{2}})

\int_{0}^{t} e^{- 2 x} d x

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