What is (\partial)/(\partial x)(3(y-1)^3(x-6)) ?

The answer to (\partial)/(\partial x)(3(y-1)^3(x-6)) is 3(y-1)^3

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(\partial)/(\partial x)(3(y-1)^3(x-6))

\frac{\partial}{\partial x} (3 (y - 1)^{3} (x - 6))

3 (y - 1)^{3}

Solution steps

\frac{\partial}{\partial x} (3 (y - 1)^{3} (x - 6))

Treat

y

as a constant

Take the constant out:

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

= 3 (y - 1)^{3} \frac{\partial}{\partial x} (x - 6)

Apply the Sum/Difference Rule:

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

= 3 (y - 1)^{3} (\frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (6))

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

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

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

Simplify

= 3 (y - 1)^{3}

\int \frac{x ^{3}}{x ^{2} + 4 x + 4} d x

\int (x - 1)^{2} - 4 d x

\int (x + 1) (x + 2) d x

x \to 1 lim (\frac{1}{x + 1})

f (x) = x^{2}, x = 0, x = 2

What is (\partial)/(\partial x)(3(y-1)^3(x-6)) ?
The answer to (\partial)/(\partial x)(3(y-1)^3(x-6)) is 3(y-1)^3