What is (\partial)/(\partial x)((y)(3x^2yz+5xz+6)) ?

The answer to (\partial)/(\partial x)((y)(3x^2yz+5xz+6)) is y(6yxz+5z)

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(\partial)/(\partial x)((y)(3x^2yz+5xz+6))

\frac{\partial}{\partial x} ((y) (3 x^{2} yz + 5 x z + 6))

y (6 y x z + 5 z)

Solution steps

\frac{\partial}{\partial x} ((y) (3 x^{2} yz + 5 x z + 6))

Treat

y, z

as constants

Take the constant out:

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

= y \frac{\partial}{\partial x} (3 x^{2} yz + 5 x z + 6)

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial x} (3 x^{2} yz) + \frac{\partial}{\partial x} (5 x z) + \frac{\partial}{\partial x} (6))

\frac{\partial}{\partial x} (3 x^{2} yz) = 6 yz x

\frac{\partial}{\partial x} (5 x z) = 5 z

\frac{\partial}{\partial x} (6) = 0

= y (6 yz x + 5 z + 0)

Simplify

= y (6 y x z + 5 z)

f ((sin (x)) 2 x - 3)

164 (3 e^{4} + 4 e^{2} + 13)

(1 + e^{t}) (- e + e^{t})

\frac{x ^{2} + 1}{3 ( x - 8 )}

7 (2 x + 6) + 2 (2 x + 6)^{'}

What is (\partial)/(\partial x)((y)(3x^2yz+5xz+6)) ?
The answer to (\partial)/(\partial x)((y)(3x^2yz+5xz+6)) is y(6yxz+5z)