What is (\partial)/(\partial v)({u}(v,w)+v*e^w) ?

The answer to (\partial)/(\partial v)({u}(v,w)+v*e^w) is (\partial)/(\partial v)({u}(v,w))+e^w

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(\partial)/(\partial v)({u}(v,w)+v*e^w)

\frac{\partial}{\partial v} (u (v, w) + v \cdot e^{w})

\frac{\partial}{\partial v} (u (v, w)) + e^{w}

Solution steps

\frac{\partial}{\partial v} (u (v, w) + v e^{w})

Treat

w

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial v} (u (v, w)) + \frac{\partial}{\partial v} (v e^{w})

\frac{\partial}{\partial v} (v e^{w}) = e^{w}

= \frac{\partial}{\partial v} (u (v, w)) + e^{w}

\int sin (2 x) e^{x} d x

p (x) = x^{4} - 3 x^{3} + 10 x^{2} - 6 x - 20

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

f (x) = 9 e^{x} + x, at x = 0

\int - e^{- 2 t} d t

What is (\partial)/(\partial v)({u}(v,w)+v*e^w) ?
The answer to (\partial)/(\partial v)({u}(v,w)+v*e^w) is (\partial)/(\partial v)({u}(v,w))+e^w