What is (\partial)/(\partial x)(x^2+5xz+3yz^2) ?

The answer to (\partial)/(\partial x)(x^2+5xz+3yz^2) is 2x+5z

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(\partial)/(\partial x)(x^2+5xz+3yz^2)

\frac{\partial}{\partial x} (x^{2} + 5 x z + 3 y z^{2})

2 x + 5 z

Solution steps

\frac{\partial}{\partial x} (x^{2} + 5 x z + 3 y z^{2})

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (5 x z) + \frac{\partial}{\partial x} (3 y z^{2})

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

\frac{\partial}{\partial x} (5 x z) = 5 z

\frac{\partial}{\partial x} (3 y z^{2}) = 0

= 2 x + 5 z + 0

Simplify

= 2 x + 5 z

f (x) = 8 ln (t^{8})

y = \frac{cos ( x )}{x ^{5}}

1 + e^{2 x}

x \to 0 + lim (\frac{x ^{2}}{7} - \frac{7}{x})

x \to 0 lim (\frac{9 ^{x} - 1 5 ^{x}}{x})

What is (\partial)/(\partial x)(x^2+5xz+3yz^2) ?
The answer to (\partial)/(\partial x)(x^2+5xz+3yz^2) is 2x+5z