What is (\partial)/(\partial x)(x^3yz^2+7yz) ?

The answer to (\partial)/(\partial x)(x^3yz^2+7yz) is 3x^2yz^2

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(\partial)/(\partial x)(x^3yz^2+7yz)

\frac{\partial}{\partial x} (x^{3} y z^{2} + 7 yz)

3 x^{2} y z^{2}

Solution steps

\frac{\partial}{\partial x} (x^{3} y z^{2} + 7 yz)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} y z^{2}) + \frac{\partial}{\partial x} (7 yz)

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

\frac{\partial}{\partial x} (7 yz) = 0

= 3 y z^{2} x^{2} + 0

Simplify

= 3 x^{2} y z^{2}

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

y^{^{''}} - 2 y^{^{'}} + y = 1

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

ln (x + 9)

t \to 0 lim (e^{- 3 t})

What is (\partial)/(\partial x)(x^3yz^2+7yz) ?
The answer to (\partial)/(\partial x)(x^3yz^2+7yz) is 3x^2yz^2