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

The answer to (\partial)/(\partial z)(xz-5x^2y^3z^4) is x-20x^2y^3z^3

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

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

x - 20 x^{2} y^{3} z^{3}

Solution steps

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

Treat

x, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial z} (5 x^{2} y^{3} z^{4}) = 20 x^{2} y^{3} z^{3}

= x - 20 x^{2} y^{3} z^{3}

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

\frac{d y}{d x} = \frac{x ^{3} - x ^{2} + x}{x}

y = tan (x) + \frac{1}{3} tan^{3} (x)

x \to - 3 lim (x^{3} + 4 x^{2} - 7)

y^{^{''}} + 4 y = e^{- x} (7 - 4 x + 5 x^{2})

What is (\partial)/(\partial z)(xz-5x^2y^3z^4) ?
The answer to (\partial)/(\partial z)(xz-5x^2y^3z^4) is x-20x^2y^3z^3