What is the derivative of (16/(sqrt(x))) ?

The derivative of (16/(sqrt(x))) is -8/(x^{3/2)}

What is the first derivative of (16/(sqrt(x))) ?

The first derivative of (16/(sqrt(x))) is -8/(x^{3/2)}

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\frac{d}{d x} (\frac{16}{x})

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

Solution steps

\frac{d}{d x} (\frac{16}{x})

Take the constant out:

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

= 16 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 16 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= 16 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

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

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

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

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

y^{^{''}} - 3 y^{^{'}} + 5 y = x e^{x}

\frac{d x}{d t} + 2 t^{3} x^{5} + \frac{x}{t} = 0

\frac{d}{d x} (5 x^{2} + sin (x) cos (x))

What is the derivative of (16/(sqrt(x))) ?
The derivative of (16/(sqrt(x))) is -8/(x^{3/2)}
What is the first derivative of (16/(sqrt(x))) ?
The first derivative of (16/(sqrt(x))) is -8/(x^{3/2)}