What is (\partial)/(\partial x)((x^2+y^2)/(z^2)) ?

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

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(\partial)/(\partial x)((x^2+y^2)/(z^2))

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{z ^{2}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{2} + y ^{2}}{z ^{2}})

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

= \frac{1}{z ^{2}} (2 x + 0)

Simplify

\frac{1}{z ^{2}} (2 x + 0) : \frac{2 x}{z ^{2}}

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

\int_{2}^{3} \frac{2 x}{( x ^{2} + 1 ) ^{3}} d x

h \to 0 lim (- 2 x - h + 8)

x \to 1 lim (\frac{x + 1}{x ^{3} - 1})

n = 5 \sum \infty \frac{2}{( n ^{2} - 1 )}

\frac{d P}{d t} = P - P^{2}

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