What is (\partial)/(\partial u)(warctan(uv)) ?

The answer to (\partial)/(\partial u)(warctan(uv)) is (wv)/(u^2v^2+1)

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(\partial)/(\partial u)(warctan(uv))

\frac{\partial}{\partial u} (w arctan (uv))

\frac{w v}{u ^{2} v ^{2} + 1}

Solution steps

\frac{\partial}{\partial u} (w arctan (uv))

Treat

w, v

as constants

Take the constant out:

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

= w \frac{\partial}{\partial u} (arctan (uv))

Apply the chain rule:

\frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

= \frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

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

= w \frac{1}{( uv ) ^{2} + 1} v

Simplify

w \frac{1}{( uv ) ^{2} + 1} v : \frac{w v}{u ^{2} v ^{2} + 1}

= \frac{w v}{u ^{2} v ^{2} + 1}

\int sinh (t) d t

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\frac{\partial}{\partial x} (y - z)

\frac{d}{d u} (e^{u})

5 t - \frac{π}{3}

What is (\partial)/(\partial u)(warctan(uv)) ?
The answer to (\partial)/(\partial u)(warctan(uv)) is (wv)/(u^2v^2+1)