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

The answer to (\partial)/(\partial x)(arctan(xy)-z) is y/(x^2y^2+1)

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

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

\frac{y}{x ^{2} y ^{2} + 1}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y}{y ^{2} x ^{2} + 1} - 0

Simplify

= \frac{y}{x ^{2} y ^{2} + 1}

x \to 0 lim (- 3 (- 6) + 3 (- 5))

y = x^{3} - 4 x, - 2 \leq x \leq 2

x \to 0 lim (\frac{x ^{2} + x}{x})

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

\int cos^{2} (x^{2}) d x

What is (\partial)/(\partial x)(arctan(xy)-z) ?
The answer to (\partial)/(\partial x)(arctan(xy)-z) is y/(x^2y^2+1)