What is (\partial)/(\partial x)(4(y-1)(x-4)^3) ?

The answer to (\partial)/(\partial x)(4(y-1)(x-4)^3) is 12(y-1)(x-4)^2

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(\partial)/(\partial x)(4(y-1)(x-4)^3)

\frac{\partial}{\partial x} (4 (y - 1) (x - 4)^{3})

12 (y - 1) (x - 4)^{2}

Solution steps

\frac{\partial}{\partial x} (4 (y - 1) (x - 4)^{3})

Treat

y

as a constant

Take the constant out:

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

= 4 (y - 1) \frac{\partial}{\partial x} ((x - 4)^{3})

Apply the chain rule:

3 (x - 4)^{2} \frac{\partial}{\partial x} (x - 4)

= 3 (x - 4)^{2} \frac{\partial}{\partial x} (x - 4)

\frac{\partial}{\partial x} (x - 4) = 1

= 4 (y - 1) \cdot 3 (x - 4)^{2} \cdot 1

Simplify

= 12 (y - 1) (x - 4)^{2}

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What is (\partial)/(\partial x)(4(y-1)(x-4)^3) ?
The answer to (\partial)/(\partial x)(4(y-1)(x-4)^3) is 12(y-1)(x-4)^2