What is the d/(d{x)}({z}arctan(({y})/({x)})) ?

The d/(d{x)}({z}arctan(({y})/({x)})) is -({y)/z}{{y}^2+{x}^2}

What is the first d/(d{x)}({z}arctan(({y})/({x)})) ?

The first d/(d{x)}({z}arctan(({y})/({x)})) is -({y)/z}{{y}^2+{x}^2}

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Popular >

\frac{d}{d x} (z arctan (\frac{y}{x}))

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

Solution steps

\frac{d}{d x} (z arctan (\frac{y}{x}))

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{( \frac{y}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{y}{x})

= \frac{1}{( \frac{y}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{y}{x})

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

= z \frac{1}{( \frac{y}{x} ) ^{2} + 1} (- \frac{y}{x ^{2}})

Simplify

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

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

\frac{e ^{x}}{e ^{x} + 1}

y^{^{''}} + 5 y = - 180 x^{2} e^{5 x}

y^{^{'}} = \frac{( 4 t + y )}{( 4 y - t )}

x + 2

x^{5} + 2, x + 2

What is the d/(d{x)}({z}arctan(({y})/({x)})) ?
The d/(d{x)}({z}arctan(({y})/({x)})) is -({y)/z}{{y}^2+{x}^2}
What is the first d/(d{x)}({z}arctan(({y})/({x)})) ?
The first d/(d{x)}({z}arctan(({y})/({x)})) is -({y)/z}{{y}^2+{x}^2}