What is (\partial)/(\partial y)((z)(x^2-5x+6y)) ?

The answer to (\partial)/(\partial y)((z)(x^2-5x+6y)) is 6z

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(\partial)/(\partial y)((z)(x^2-5x+6y))

\frac{\partial}{\partial y} ((z) (x^{2} - 5 x + 6 y))

6 z

Solution steps

\frac{\partial}{\partial y} ((z) (x^{2} - 5 x + 6 y))

Treat

z, x

as constants

Take the constant out:

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

= z \frac{\partial}{\partial y} (x^{2} - 5 x + 6 y)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial y} (x^{2}) - \frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (6 y))

\frac{\partial}{\partial y} (x^{2}) = 0

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

\frac{\partial}{\partial y} (6 y) = 6

= z (0 - 0 + 6)

Simplify

= 6 z

(- 5 - 5 cos (θ))^{2} \cdot \frac{1}{2}

(x - 3) 2 x^{3} - 3 x^{2} - 5 x - 12

(z^{2} - 8) e^{3 - z}

cos (3 t) (u (t - 4 π))

\frac{( 4 x + 1 ) ^{3}}{12}

What is (\partial)/(\partial y)((z)(x^2-5x+6y)) ?
The answer to (\partial)/(\partial y)((z)(x^2-5x+6y)) is 6z