What is (\partial)/(\partial y)(3xyz+xy^2-xz^3) ?

The answer to (\partial)/(\partial y)(3xyz+xy^2-xz^3) is 3xz+2xy

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(\partial)/(\partial y)(3xyz+xy^2-xz^3)

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

3 x z + 2 x y

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (x z^{3}) = 0

= 3 x z + 2 x y - 0

Simplify

= 3 x z + 2 x y

42 y^{^{''}} + 29 y^{^{'}} - 5 y = 0

n = 1 \sum \infty \frac{n}{( 3 + n )}

\frac{d}{d x} (ln (3 x^{3} + x + 6))

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

\frac{16}{( 1 - x ) ^{3}}

What is (\partial)/(\partial y)(3xyz+xy^2-xz^3) ?
The answer to (\partial)/(\partial y)(3xyz+xy^2-xz^3) is 3xz+2xy