What is (\partial)/(\partial x)((6x+3y)ey) ?

The answer to (\partial)/(\partial x)((6x+3y)ey) is 6ey

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(\partial)/(\partial x)((6x+3y)ey)

\frac{\partial}{\partial x} ((6 x + 3 y) ey)

6 ey

Solution steps

\frac{\partial}{\partial x} ((6 x + 3 y) ey)

Treat

y

as a constant

Take the constant out:

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

= ey \frac{\partial}{\partial x} (6 x + 3 y)

Apply the Sum/Difference Rule:

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

= ey (\frac{\partial}{\partial x} (6 x) + \frac{\partial}{\partial x} (3 y))

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

\frac{\partial}{\partial x} (3 y) = 0

= ey (6 + 0)

Simplify

= 6 ey

\int \frac{1}{( x - 3 ) ( x + 2 )} d x

s l o p e (1, 6), (0.5, 8)

x \to 0 lim ((1 - 2 x)^{\frac{1}{2}})

in v erse l a pl a ce \frac{150}{s ( s ^{2} + 8 s + 25 )}

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

What is (\partial)/(\partial x)((6x+3y)ey) ?
The answer to (\partial)/(\partial x)((6x+3y)ey) is 6ey