What is (\partial)/(\partial x)(x^9yz^2+9yz) ?

The answer to (\partial)/(\partial x)(x^9yz^2+9yz) is 9x^8yz^2

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(\partial)/(\partial x)(x^9yz^2+9yz)

\frac{\partial}{\partial x} (x^{9} y z^{2} + 9 yz)

9 x^{8} y z^{2}

Solution steps

\frac{\partial}{\partial x} (x^{9} y z^{2} + 9 yz)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{9} y z^{2}) + \frac{\partial}{\partial x} (9 yz)

\frac{\partial}{\partial x} (x^{9} y z^{2}) = 9 y z^{2} x^{8}

\frac{\partial}{\partial x} (9 yz) = 0

= 9 y z^{2} x^{8} + 0

Simplify

= 9 x^{8} y z^{2}

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

\int \frac{1}{1 + 2 u} d u

\int (3 x^{2} - 4 x + 7) d x

f (x) = (\frac{x ^{2} + 4}{x ^{2} - 4})^{4}

\frac{d y}{d x} = \frac{( x y + 3 x - y - 3 )}{( x y - 2 x + 4 y - 8 )}

What is (\partial)/(\partial x)(x^9yz^2+9yz) ?
The answer to (\partial)/(\partial x)(x^9yz^2+9yz) is 9x^8yz^2