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

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

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

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

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derivative of

\frac{y ^{\frac{3}{2}}}{3} - y^{\frac{1}{2}}

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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