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

The derivative of 3/2 x^{1/2}-1/3 x^{2/3} is 3/(4x^{1/2)}-2/(9x^{1/3)}

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

The first derivative of 3/2 x^{1/2}-1/3 x^{2/3} is 3/(4x^{1/2)}-2/(9x^{1/3)}

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

\frac{3}{4 x ^{\frac{1}{2}}} - \frac{2}{9 x ^{\frac{1}{3}}}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{3 x ^{\frac{1}{2}}}{2}) = \frac{3}{4 x ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{x ^{\frac{2}{3}}}{3}) = \frac{2}{9 x ^{\frac{1}{3}}}

= \frac{3}{4 x ^{\frac{1}{2}}} - \frac{2}{9 x ^{\frac{1}{3}}}

t \to 0 lim (\frac{2}{1 + t})

\frac{\partial}{\partial x} (e^{x} y)

\int_{0}^{8} (1 + 3 x) d x

\int e^{\frac{3}{x}} d x

\frac{s - 6}{3 s ^{2} + s + 12}

What is the derivative of 3/2 x^{1/2}-1/3 x^{2/3} ?
The derivative of 3/2 x^{1/2}-1/3 x^{2/3} is 3/(4x^{1/2)}-2/(9x^{1/3)}
What is the first derivative of 3/2 x^{1/2}-1/3 x^{2/3} ?
The first derivative of 3/2 x^{1/2}-1/3 x^{2/3} is 3/(4x^{1/2)}-2/(9x^{1/3)}