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

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

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(\partial)/(\partial x)(x^7yz^2+6yz)

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

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

Solution steps

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

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

\frac{\partial}{\partial x} (6 yz) = 0

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

Simplify

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

\frac{\partial}{\partial x} (e^{- (x^{7} + y^{7})})

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

x \to \infty lim (e^{7 x})

(9 - x^{2})^{- \frac{1}{2}}

y = 2 x^{2} + 9 x - 7

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