What is (\partial)/(\partial x)(x-z-arctan(yz)) ?

The answer to (\partial)/(\partial x)(x-z-arctan(yz)) is 1

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(\partial)/(\partial x)(x-z-arctan(yz))

\frac{\partial}{\partial x} (x - z - arctan (yz))

1

Solution steps

\frac{\partial}{\partial x} (x - z - arctan (yz))

Treat

z, y

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (z) - \frac{\partial}{\partial x} (arctan (yz))

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

\frac{\partial}{\partial x} (z) = 0

\frac{\partial}{\partial x} (arctan (yz)) = 0

= 1 - 0 - 0

Simplify

= 1

f (x) = \frac{x ^{3}}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} (\frac{cos ( x )}{x})

\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

y^{^{'}} - \frac{3 y}{x} = x

sin (x^{2}) + \frac{( 1 - x )}{1 + x}

What is (\partial)/(\partial x)(x-z-arctan(yz)) ?
The answer to (\partial)/(\partial x)(x-z-arctan(yz)) is 1