What is the derivative of 2/3 (x^{3/2}+y^{3/2}) ?

The derivative of 2/3 (x^{3/2}+y^{3/2}) is x^{1/2}+(dy)/(dx)y^{1/2}

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

The first derivative of 2/3 (x^{3/2}+y^{3/2}) is x^{1/2}+(dy)/(dx)y^{1/2}

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\frac{d}{d x} (\frac{2}{3} (x^{\frac{3}{2}} + y^{\frac{3}{2}}))

x^{\frac{1}{2}} + \frac{d y}{d x} y^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (\frac{2}{3} (x^{\frac{3}{2}} + y^{\frac{3}{2}}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

\frac{2}{3} (\frac{3 x ^{\frac{1}{2}}}{2} + \frac{3 \frac{d y}{d x} y ^{\frac{1}{2}}}{2}) : x^{\frac{1}{2}} + \frac{d y}{d x} y^{\frac{1}{2}}

= x^{\frac{1}{2}} + \frac{d y}{d x} y^{\frac{1}{2}}

e^{t - 1}

f (x) = \frac{- 2 ln ( x ) + 1}{x ^{3}}

ln (1 - 5 y)

\int_{0}^{2} \frac{1}{4 - t ^{2}} d t

What is the derivative of 2/3 (x^{3/2}+y^{3/2}) ?
The derivative of 2/3 (x^{3/2}+y^{3/2}) is x^{1/2}+(dy)/(dx)y^{1/2}
What is the first derivative of 2/3 (x^{3/2}+y^{3/2}) ?
The first derivative of 2/3 (x^{3/2}+y^{3/2}) is x^{1/2}+(dy)/(dx)y^{1/2}