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

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

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

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

6 (y - 3) (x - 2)^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - 2) = 1

= 2 (y - 3) \cdot 3 (x - 2)^{2} \cdot 1

Simplify

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

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