What is (\partial)/(\partial x)((4-z^2)/(3x)) ?

The answer to (\partial)/(\partial x)((4-z^2)/(3x)) is -(4-z^2)/(3x^2)

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(\partial)/(\partial x)((4-z^2)/(3x))

\frac{\partial}{\partial x} (\frac{4 - z ^{2}}{3 x})

- \frac{4 - z ^{2}}{3 x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{4 - z ^{2}}{3 x})

Treat

z

as a constant

Take the constant out:

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

= \frac{4 - z ^{2}}{3} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= \frac{4 - z ^{2}}{3} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= \frac{4 - z ^{2}}{3} (- 1 \cdot x^{- 1 - 1})

Simplify

\frac{4 - z ^{2}}{3} (- 1 \cdot x^{- 1 - 1}) : - \frac{4 - z ^{2}}{3 x ^{2}}

= - \frac{4 - z ^{2}}{3 x ^{2}}

\int \frac{x ^{2} + 3 x - 5}{x - 3} d x

x \to 5 + lim (\frac{2 - x}{x - 5})

\int - 4 x (- 6 x^{2} - 1)^{6} d x

\frac{d}{d x} (x^{2} - \frac{2}{3} x^{3})

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

What is (\partial)/(\partial x)((4-z^2)/(3x)) ?
The answer to (\partial)/(\partial x)((4-z^2)/(3x)) is -(4-z^2)/(3x^2)