What is (\partial)/(\partial x)(1/(4x)) ?

The answer to (\partial)/(\partial x)(1/(4x)) is -1/(4x^2)

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(\partial)/(\partial x)(1/(4x))

\frac{\partial}{\partial x} (\frac{1}{4 x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{1}{4 x})

Take the constant out:

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

= \frac{1}{4} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{4} (- 1 \cdot x^{- 1 - 1}) : - \frac{1}{4 x ^{2}}

= - \frac{1}{4 x ^{2}}

\frac{\partial}{\partial x} (3 x e^{7 x y})

\int_{0}^{7} \frac{4 t}{( t - 8 ) ^{2}} d t

n = 0 \sum \infty \frac{1}{n ^{3}}

\frac{d}{d x} (\frac{4}{x - 1})

\int (x - 1)^{2} x d x

What is (\partial)/(\partial x)(1/(4x)) ?
The answer to (\partial)/(\partial x)(1/(4x)) is -1/(4x^2)