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

The answer to (\partial)/(\partial x)(x^7yz^2+7yz) is 7x^6yz^2

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

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

7 x^{6} y z^{2}

Solution steps

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

\frac{\partial}{\partial x} (x^{7} y z^{2}) = 7 y z^{2} x^{6}

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

= 7 y z^{2} x^{6} + 0

Simplify

= 7 x^{6} y z^{2}

a re a x = y, x = - y^{2} + 6 y

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\frac{\partial}{\partial x} (e^{- 3 x - y})

What is (\partial)/(\partial x)(x^7yz^2+7yz) ?
The answer to (\partial)/(\partial x)(x^7yz^2+7yz) is 7x^6yz^2