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

The answer to (\partial)/(\partial x)(3/(2x^2)) is -3/(x^3)

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(\partial)/(\partial x)(3/(2x^2))

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

- \frac{3}{x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{3}{x ^{3}}

y^{2} y^{^{'}} = x^{2}

\int_{0}^{\frac{π}{3}} x sin (12 x) d x

\int x^{\frac{2}{3}} d x

f (x) = \frac{sin ^{2} ( x )}{x ^{2}}

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

What is (\partial)/(\partial x)(3/(2x^2)) ?
The answer to (\partial)/(\partial x)(3/(2x^2)) is -3/(x^3)