What is (\partial)/(\partial t)((u)((tu-v)^2ln(w-uv))) ?

The answer to (\partial)/(\partial t)((u)((tu-v)^2ln(w-uv))) is 2u^2ln(w-uv)(ut-v)

Popular >

(\partial)/(\partial t)((u)((tu-v)^2ln(w-uv)))

\frac{\partial}{\partial t} ((u) ((t u - v)^{2} ln (w - uv)))

2 u^{2} ln (w - uv) (u t - v)

Solution steps

\frac{\partial}{\partial t} ((u) ((t u - v)^{2} ln (w - uv)))

Treat

u, v, w

as constants

Take the constant out:

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

= u ln (w - uv) \frac{\partial}{\partial t} ((t u - v)^{2})

Apply the chain rule:

2 (t u - v) \frac{\partial}{\partial t} (t u - v)

= 2 (t u - v) \frac{\partial}{\partial t} (t u - v)

\frac{\partial}{\partial t} (t u - v) = u

= u ln (w - uv) \cdot 2 (t u - v) u

Simplify

u ln (w - uv) \cdot 2 (t u - v) u : 2 u^{2} ln (w - uv) (u t - v)

= 2 u^{2} ln (w - uv) (u t - v)

\frac{0.5 - \frac{1}{z}}{z ^{3} - 1.3 z ^{2} + 0.4 z} \cdot \frac{z}{z}

\frac{7 s ^{2} + 63 s + 134}{( s + 3 ) ( s + 4 ) ( s + 5 )}

\frac{a ( x + 1 ) ^{2} + b ( x ) ( x + 1 ) + c x}{x ( x + 1 ) ^{2}}

\frac{2 + v}{( v + 1 ) ( v + 4 )}

sin (x (π - \frac{π}{2 ^{x}}))

What is (\partial)/(\partial t)((u)((tu-v)^2ln(w-uv))) ?
The answer to (\partial)/(\partial t)((u)((tu-v)^2ln(w-uv))) is 2u^2ln(w-uv)(ut-v)