What is (\partial)/(\partial x)(3(y+4)(x-5)^3) ?

The answer to (\partial)/(\partial x)(3(y+4)(x-5)^3) is 9(y+4)(x-5)^2

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(\partial)/(\partial x)(3(y+4)(x-5)^3)

\frac{\partial}{\partial x} (3 (y + 4) (x - 5)^{3})

9 (y + 4) (x - 5)^{2}

Solution steps

\frac{\partial}{\partial x} (3 (y + 4) (x - 5)^{3})

Treat

y

as a constant

Take the constant out:

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

= 3 (y + 4) \frac{\partial}{\partial x} ((x - 5)^{3})

Apply the chain rule:

3 (x - 5)^{2} \frac{\partial}{\partial x} (x - 5)

= 3 (x - 5)^{2} \frac{\partial}{\partial x} (x - 5)

\frac{\partial}{\partial x} (x - 5) = 1

= 3 (y + 4) \cdot 3 (x - 5)^{2} \cdot 1

Simplify

= 9 (y + 4) (x - 5)^{2}

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What is (\partial)/(\partial x)(3(y+4)(x-5)^3) ?
The answer to (\partial)/(\partial x)(3(y+4)(x-5)^3) is 9(y+4)(x-5)^2