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

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

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

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

z (4 x^{2} + 3)

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (3 y) = 3

\frac{\partial}{\partial y} (5) = 0

= z (4 x^{2} + 3 - 0)

Simplify

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

(x + y - 1) d x - (2 x - y + 1) d y

\frac{x ^{2} + 2 x}{( x + 1 ) ( x ^{2} + 4 )}

e^{p} (p + p p)

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

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

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