What is the derivative of (-3)/(2x) ?

The derivative of (-3)/(2x) is 3/(2x^2)

What is the first derivative of (-3)/(2x) ?

The first derivative of (-3)/(2x) is 3/(2x^2)

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derivative of

\frac{- 3}{2 x}

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{3}{2 x ^{2}}

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

\int_{0}^{4} x - 1 d x

y = 5 - x^{2}

\int (6 x + 5) 3 x^{2} + 5 x d x

What is the derivative of (-3)/(2x) ?
The derivative of (-3)/(2x) is 3/(2x^2)
What is the first derivative of (-3)/(2x) ?
The first derivative of (-3)/(2x) is 3/(2x^2)