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

The derivative of 1/3 x^{(1/2}-x^{(3/2)}) is 1/(6x^{1/2)}-(3x^{1/2})/2

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

The first derivative of 1/3 x^{(1/2}-x^{(3/2)}) is 1/(6x^{1/2)}-(3x^{1/2})/2

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

\frac{1}{6 x ^{\frac{1}{2}}} - \frac{3 x ^{\frac{1}{2}}}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{3}) = \frac{1}{6 x ^{\frac{1}{2}}}

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

= \frac{1}{6 x ^{\frac{1}{2}}} - \frac{3 x ^{\frac{1}{2}}}{2}

f (x) = \frac{1}{x}, at x = \frac{1}{4}

\int (ln (t)) d t

\frac{8}{( x ^{2} + 4 )}

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

f (x) = x \cdot e^{- x + 1}

What is the derivative of 1/3 x^{(1/2}-x^{(3/2)}) ?
The derivative of 1/3 x^{(1/2}-x^{(3/2)}) is 1/(6x^{1/2)}-(3x^{1/2})/2
What is the first derivative of 1/3 x^{(1/2}-x^{(3/2)}) ?
The first derivative of 1/3 x^{(1/2}-x^{(3/2)}) is 1/(6x^{1/2)}-(3x^{1/2})/2