What is (\partial)/(\partial x)(-sqrt(2x)) ?

The answer to (\partial)/(\partial x)(-sqrt(2x)) is -1/(sqrt(2)\sqrt{x)}

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(\partial)/(\partial x)(-sqrt(2x))

\frac{\partial}{\partial x} (- 2 x)

- \frac{1}{2 x}

Solution steps

\frac{\partial}{\partial x} (- 2 x)

Simplify

- 2 x : - 2 x

= \frac{\partial}{\partial x} (- 2 x)

Take the constant out:

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

= - 2 \frac{\partial}{\partial x} (x)

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

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

= - 2 \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

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

= - \frac{1}{2 x}

\frac{\partial}{\partial y} (x^{2} + x y^{3})

5 \frac{d y}{d t} + y = 20 t

\int e^{5 - 2 x} d x

\frac{d}{d x} (x^{2} ln (x) + x^{3})

\frac{d y}{d x} (x) = y

What is (\partial)/(\partial x)(-sqrt(2x)) ?
The answer to (\partial)/(\partial x)(-sqrt(2x)) is -1/(sqrt(2)\sqrt{x)}