What is (\partial)/(\partial x)(1/3 x^{3/2}) ?

The answer to (\partial)/(\partial x)(1/3 x^{3/2}) is (x^{1/2})/2

Popular >

(\partial)/(\partial x)(1/3 x^{3/2})

\frac{\partial}{\partial x} (\frac{1}{3} x^{\frac{3}{2}})

\frac{x ^{\frac{1}{2}}}{2}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{3} x^{\frac{3}{2}})

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

\frac{\partial}{\partial y} (6 x cos (x) cos (y))

y^{^{'}} + y = - x

x \to 0 lim \frac{( ( 6 + x ) ^{- 1} - 6 ^{- 1} )}{x}

f (x) = \frac{x ^{2} - 6 x + 12}{x - 4}

x^{2} - 3 x

What is (\partial)/(\partial x)(1/3 x^{3/2}) ?
The answer to (\partial)/(\partial x)(1/3 x^{3/2}) is (x^{1/2})/2