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

The derivative of 2/3 x^{3/2}-1/2 x^{1/2} is (-1+4x)/(4x^{1/2)}

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

The first derivative of 2/3 x^{3/2}-1/2 x^{1/2} is (-1+4x)/(4x^{1/2)}

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

\frac{- 1 + 4 x}{4 x ^{\frac{1}{2}}}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{x ^{\frac{1}{2}}}{2}) = \frac{1}{4 x ^{\frac{1}{2}}}

= x^{\frac{1}{2}} - \frac{1}{4 x ^{\frac{1}{2}}}

Simplify

x^{\frac{1}{2}} - \frac{1}{4 x ^{\frac{1}{2}}} : \frac{- 1 + 4 x}{4 x ^{\frac{1}{2}}}

= \frac{- 1 + 4 x}{4 x ^{\frac{1}{2}}}

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

\frac{d}{d x} (\frac{1}{4} e^{- x} + e^{x})

f (x) = x x + 1

x \to 0 lim (\frac{7 ^{x} - 1}{x})

\int \frac{( 5 + x + x )}{x} d x

What is the derivative of 2/3 x^{3/2}-1/2 x^{1/2} ?
The derivative of 2/3 x^{3/2}-1/2 x^{1/2} is (-1+4x)/(4x^{1/2)}
What is the first derivative of 2/3 x^{3/2}-1/2 x^{1/2} ?
The first derivative of 2/3 x^{3/2}-1/2 x^{1/2} is (-1+4x)/(4x^{1/2)}