What is (\partial)/(\partial x)(2*(y-2)^3*(x-6)) ?

The answer to (\partial)/(\partial x)(2*(y-2)^3*(x-6)) is 2(y-2)^3

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(\partial)/(\partial x)(2(y-2)^3(x-6))

\frac{\partial}{\partial x} (2 \cdot (y - 2)^{3} \cdot (x - 6))

2 (y - 2)^{3}

Solution steps

\frac{\partial}{\partial x} (2 (y - 2)^{3} (x - 6))

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 2 (y - 2)^{3} (1 - 0)

Simplify

= 2 (y - 2)^{3}

What is (\partial)/(\partial x)(2*(y-2)^3*(x-6)) ?
The answer to (\partial)/(\partial x)(2*(y-2)^3*(x-6)) is 2(y-2)^3