What is the derivative of-A/(2x^{3/2}) ?

The derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}

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

The first derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}

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

\frac{3 A}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- \frac{A}{2} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : \frac{3 A}{4 x ^{\frac{5}{2}}}

= \frac{3 A}{4 x ^{\frac{5}{2}}}

x \to 4 lim (\frac{x ^{2} - 1}{x - 4})

\frac{d}{d x} (- x^{- x})

\frac{\partial}{\partial y} (cos (x) cos (y) + 2 x)

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

\frac{d y}{d t} - \frac{2}{t} y = t^{5}

What is the derivative of-A/(2x^{3/2}) ?
The derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}
What is the first derivative of-A/(2x^{3/2}) ?
The first derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}