What is (\partial)/(\partial u)((x)(u+v)) ?

The answer to (\partial)/(\partial u)((x)(u+v)) is x

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(\partial)/(\partial u)((x)(u+v))

\frac{\partial}{\partial u} ((x) (u + v))

x

Solution steps

\frac{\partial}{\partial u} ((x) (u + v))

Treat

x, v

as constants

Take the constant out:

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

= x \frac{\partial}{\partial u} (u + v)

Apply the Sum/Difference Rule:

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

= x (\frac{\partial}{\partial u} (u) + \frac{\partial}{\partial u} (v))

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

\frac{\partial}{\partial u} (v) = 0

= x (1 + 0)

Simplify

= x

(- x y sin (x) + 2 y cos (x)) d x + 2 x cos (x) d y

\frac{1}{( y + 1 ) ^{2}}

(x - \frac{7}{2})^{2}

(5 x - 2 y) l e f t (5 x + 2 y)

\frac{( x ( x - 8 ) )}{( x + 1 )}

What is (\partial)/(\partial u)((x)(u+v)) ?
The answer to (\partial)/(\partial u)((x)(u+v)) is x