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

The answer to (\partial)/(\partial x)(xz-5x^2y^3z^4) is z-10z^4y^3x

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

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

z - 10 z^{4} y^{3} x

Solution steps

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

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (5 x^{2} y^{3} z^{4}) = 10 z^{4} y^{3} x

= z - 10 z^{4} y^{3} x

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

\int \frac{cos ( x )}{sin ^{2} ( x ) - 36} d x

y^{^{''}} + 2 y^{^{'}} + 122 y = 0

\frac{\partial}{\partial x} (sin (- e^{y}))

\frac{d}{d x} (cos (\frac{3 x}{2}))

What is (\partial)/(\partial x)(xz-5x^2y^3z^4) ?
The answer to (\partial)/(\partial x)(xz-5x^2y^3z^4) is z-10z^4y^3x