What is the derivative of (-1/(4x^{3/2)}) ?

The derivative of (-1/(4x^{3/2)}) is 3/(8x^{5/2)}

What is the first derivative of (-1/(4x^{3/2)}) ?

The first derivative of (-1/(4x^{3/2)}) is 3/(8x^{5/2)}

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\frac{d}{d x} (\frac{- 1}{4 x ^{\frac{3}{2}}})

\frac{3}{8 x ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{- 1}{4 x ^{\frac{3}{2}}})

Simplify

\frac{- 1}{4 x ^{\frac{3}{2}}} : - \frac{1}{4 x ^{\frac{3}{2}}}

= \frac{d}{d x} (- \frac{1}{4 x ^{\frac{3}{2}}})

Take the constant out:

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

= - \frac{1}{4} \frac{d}{d x} (\frac{1}{x ^{\frac{3}{2}}})

Apply exponent rule:

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

= - \frac{1}{4} \frac{d}{d x} (x^{- \frac{3}{2}})

Apply the Power Rule:

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

= - \frac{1}{4} (- \frac{3}{2} x^{- \frac{3}{2} - 1})

Simplify

- \frac{1}{4} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : \frac{3}{8 x ^{\frac{5}{2}}}

= \frac{3}{8 x ^{\frac{5}{2}}}

n = 0 \sum \infty \frac{1}{2 n}

\int x^{2} - x^{4} d x

(x, y) \to (0, 0) lim (\frac{x ^{10} - y ^{10}}{x ^{5} + y ^{5}})

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 9 e^{x}

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

What is the derivative of (-1/(4x^{3/2)}) ?
The derivative of (-1/(4x^{3/2)}) is 3/(8x^{5/2)}
What is the first derivative of (-1/(4x^{3/2)}) ?
The first derivative of (-1/(4x^{3/2)}) is 3/(8x^{5/2)}