What is the derivative of 1/(x 3/2) ?

The derivative of 1/(x 3/2) is -2/(3x^2)

What is the first derivative of 1/(x 3/2) ?

The first derivative of 1/(x 3/2) is -2/(3x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

(t e^{- t})^{^{'}}

\frac{\partial}{\partial x} (r cos (t))

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.8 y), y (1) = 0.7

\frac{d}{d x} (18 x + ln (18 x))

n = 0 \sum \infty \frac{n}{4 ^{n}}

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