What is (\partial)/(\partial x)((z)(x^2y+3xy^4)) ?

The answer to (\partial)/(\partial x)((z)(x^2y+3xy^4)) is z(2yx+3y^4)

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(\partial)/(\partial x)((z)(x^2y+3xy^4))

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

z (2 y x + 3 y^{4})

Solution steps

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

Treat

z, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x y^{4}) = 3 y^{4}

= z (2 y x + 3 y^{4})

(sec (x) + csc (x))^{2}

sin (x) (cot (x) + csc (x))

(x - 2) (x - 3)

\frac{x ^{2} - 7 x + 9}{( x - 3 ) ^{2}}

\frac{1 - e ^{- 2 s}}{s ( s ^{2} + 2 s + 5 )}

What is (\partial)/(\partial x)((z)(x^2y+3xy^4)) ?
The answer to (\partial)/(\partial x)((z)(x^2y+3xy^4)) is z(2yx+3y^4)