What is (\partial)/(\partial y)(xz-5x^2y^3z^4) ?

The answer to (\partial)/(\partial y)(xz-5x^2y^3z^4) is -15x^2z^4y^2

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(\partial)/(\partial y)(xz-5x^2y^3z^4)

\frac{\partial}{\partial y} (x z - 5 x^{2} y^{3} z^{4})

- 15 x^{2} z^{4} y^{2}

Solution steps

\frac{\partial}{\partial y} (x z - 5 x^{2} y^{3} z^{4})

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x z) - \frac{\partial}{\partial y} (5 x^{2} y^{3} z^{4})

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

\frac{\partial}{\partial y} (5 x^{2} y^{3} z^{4}) = 15 x^{2} z^{4} y^{2}

= 0 - 15 x^{2} z^{4} y^{2}

Simplify

= - 15 x^{2} z^{4} y^{2}

\frac{d}{d x} (\frac{- 10 x + 4}{3 x - 8})

y = x^{2} + x

\int (x + y) d x

\frac{d y}{d x}, (3 x y + 7)^{2} = 6 y

\int sec^{2} (θ) tan^{2} (θ) d θ

What is (\partial)/(\partial y)(xz-5x^2y^3z^4) ?
The answer to (\partial)/(\partial y)(xz-5x^2y^3z^4) is -15x^2z^4y^2