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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derivative of

- \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}}})

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}}}

y^{^{''}} + 8 y^{^{'}} + 20 y = 0

\frac{d}{d x} (x^{\frac{1}{4}} cos (7 ln (x)))

\frac{\partial}{\partial x} (\frac{x}{y ^{2}} sin (\frac{x}{y}))

\int_{1}^{4} 7 t ln (t) d t

y = (7 ln (x))^{2}

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)}