What is (\partial)/(\partial x)(xy^2z^3-8) ?

The answer to (\partial)/(\partial x)(xy^2z^3-8) is y^2z^3

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(\partial)/(\partial x)(xy^2z^3-8)

\frac{\partial}{\partial x} (x y^{2} z^{3} - 8)

y^{2} z^{3}

Solution steps

\frac{\partial}{\partial x} (x y^{2} z^{3} - 8)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y^{2} z^{3}) - \frac{\partial}{\partial x} (8)

\frac{\partial}{\partial x} (x y^{2} z^{3}) = y^{2} z^{3}

\frac{\partial}{\partial x} (8) = 0

= y^{2} z^{3} - 0

Simplify

= y^{2} z^{3}

\int \frac{6 x ^{2} + x + 55}{( x + 1 ) ( x ^{2} + 9 )} d x

\int y (1 - x^{2}) d y

\frac{d}{d x} ((5 x - 1) (6 x - 3)^{- 1})

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

What is (\partial)/(\partial x)(xy^2z^3-8) ?
The answer to (\partial)/(\partial x)(xy^2z^3-8) is y^2z^3