What is (\partial)/(\partial x)((u(x,t))(3x-2t)) ?

The answer to (\partial)/(\partial x)((u(x,t))(3x-2t)) is u((,t*1)(3x-2t)+3(x,t))

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(\partial)/(\partial x)((u(x,t))(3x-2t))

\frac{\partial}{\partial x} ((u (x, t)) (3 x - 2 t))

u ((, t \cdot 1) (3 x - 2 t) + 3 (x, t))

Solution steps

\frac{\partial}{\partial x} ((u (x, t)) (3 x - 2 t))

Treat

u, t

as constants

Take the constant out:

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

= u \frac{\partial}{\partial x} ((x, t) (3 x - 2 t))

Apply the Product Rule:

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

f = x, t, g = 3 x - 2 t

= u (\frac{\partial}{\partial x} (x, t) (3 x - 2 t) + \frac{\partial}{\partial x} (3 x - 2 t) (x, t))

\frac{\partial}{\partial x} (x, t) = (, t \cdot 1)

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

= u ((, t \cdot 1) (3 x - 2 t) + 3 (x, t))

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

\frac{( 16 x ^{6} - 9 ) ^{2}}{576 x ^{6}}

\frac{7 n ^{2} + n ^{4} - 4 x ^{3}}{( x ^{4} + n ^{4} ) ^{2}}

\frac{( x ^{4} - 4 ) ^{2}}{16 x ^{4}}

Dr (π r^{2} + a r)

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