What is (\partial)/(\partial x)(x^9yz^2+5yz) ?

The answer to (\partial)/(\partial x)(x^9yz^2+5yz) is 9x^8yz^2

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(\partial)/(\partial x)(x^9yz^2+5yz)

\frac{\partial}{\partial x} (x^{9} y z^{2} + 5 yz)

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

Solution steps

\frac{\partial}{\partial x} (x^{9} y z^{2} + 5 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} (5 yz)

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

\frac{\partial}{\partial x} (5 yz) = 0

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

Simplify

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

\int cos^{3} (2 x) sin^{3} (2 x) d x

cos (y) y^{^{'}} = e^{2 x} + 1

\frac{y ^{3}}{30} + \frac{5}{2 y}

ln (1 + x)

\int 1 + cos (t) d t

What is (\partial)/(\partial x)(x^9yz^2+5yz) ?
The answer to (\partial)/(\partial x)(x^9yz^2+5yz) is 9x^8yz^2