What is (\partial)/(\partial x)(xy+z(x+2y-1)) ?

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

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(\partial)/(\partial x)(xy+z(x+2y-1))

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

y + z

Solution steps

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

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} (z (x + 2 y - 1))

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

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

= y + z

a re a x + y = 2, y = x^{2}

x \to 3 lim (\frac{x + 4}{x - 3})

y^{^{''}} - 8 y^{^{'}} + 52 y = 0

\int e^{- s t} 1 d t

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

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