What is (\partial)/(\partial x)(xy+yz+zx-3) ?

The answer to (\partial)/(\partial x)(xy+yz+zx-3) is y+z

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(\partial)/(\partial x)(xy+yz+zx-3)

\frac{\partial}{\partial x} (x y + yz + z x - 3)

y + z

Solution steps

\frac{\partial}{\partial x} (x y + yz + z x - 3)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (yz) + \frac{\partial}{\partial x} (z x) - \frac{\partial}{\partial x} (3)

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

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

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

\frac{\partial}{\partial x} (3) = 0

= y + 0 + z - 0

Simplify

= y + z

y = e^{2 x}, at x = \frac{1}{2} ln (2)

x \to - 1 lim (\frac{∣ x ∣}{x + 1})

\int x arctan (8 x) d x

f (x) = cos^{2} (4 x)

\frac{d}{d x} ((6 x + e^{- x^{2}})^{5})

What is (\partial)/(\partial x)(xy+yz+zx-3) ?
The answer to (\partial)/(\partial x)(xy+yz+zx-3) is y+z