What is (\partial)/(\partial x)((u)(3x(x-1))) ?

The answer to (\partial)/(\partial x)((u)(3x(x-1))) is 3u(2x-1)

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(\partial)/(\partial x)((u)(3x(x-1)))

\frac{\partial}{\partial x} ((u) (3 x (x - 1)))

3 u (2 x - 1)

Solution steps

\frac{\partial}{\partial x} ((u) (3 x (x - 1)))

Treat

u

as a constant

Take the constant out:

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

= u \cdot 3 \frac{\partial}{\partial x} (x (x - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x - 1

= u \cdot 3 (\frac{\partial}{\partial x} (x) (x - 1) + \frac{\partial}{\partial x} (x - 1) x)

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

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

= u \cdot 3 (1 \cdot (x - 1) + 1 \cdot x)

Simplify

u \cdot 3 (1 \cdot (x - 1) + 1 \cdot x) : 3 u (2 x - 1)

= 3 u (2 x - 1)

(5, 6, 8) - (7 i + 6 j)

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\frac{3 ( 2 x - 1 ) ^{2}}{2 x}

\frac{3 x ^{2} - 6 x + 2}{2 ( 4 - 3 y ^{2} + 2 y ^{3} - 4 y )}

\frac{2}{( x - 2 ) ( x - 5 )}

What is (\partial)/(\partial x)((u)(3x(x-1))) ?
The answer to (\partial)/(\partial x)((u)(3x(x-1))) is 3u(2x-1)