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

The answer to (\partial)/(\partial x)(x^5yz^2+2yz) is 5x^4yz^2

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

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

5 x^{4} y z^{2}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{5} y z^{2}) = 5 y z^{2} x^{4}

\frac{\partial}{\partial x} (2 yz) = 0

= 5 y z^{2} x^{4} + 0

Simplify

= 5 x^{4} y z^{2}

\frac{d}{d x} (\frac{3 x ^{2} - x + 1}{x ^{7}})

\int \frac{1}{x 36 x ^{2} + 1} d x

y^{^{'}} = - y^{\frac{1}{3}}

\frac{d}{d x} (2 sin (x) - x)

(- \frac{5}{2}, 1), (- \frac{1}{2}, 4)

What is (\partial)/(\partial x)(x^5yz^2+2yz) ?
The answer to (\partial)/(\partial x)(x^5yz^2+2yz) is 5x^4yz^2