What is (\partial)/(\partial x)(z/x) ?

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

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(\partial)/(\partial x)(z/x)

\frac{\partial}{\partial x} (\frac{z}{x})

- \frac{z}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{z}{x})

Treat

z

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= z (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

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\int - cos (y) d y

n = 0 \sum \infty 4 \cdot (- \frac{1}{8})^{n}

y \to - 2 lim (\frac{y ^{3} + 8}{y + 2})

\int cos (x) sec (x) tan (x) d x

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