What is (\partial)/(\partial u)(u^2-v^2) ?

The answer to (\partial)/(\partial u)(u^2-v^2) is 2u

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(\partial)/(\partial u)(u^2-v^2)

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

2 u

Solution steps

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

Treat

v

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial u} (u^{2}) = 2 u

\frac{\partial}{\partial u} (v^{2}) = 0

= 2 u - 0

Simplify

= 2 u

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

\frac{1}{1 + t}

\frac{2 x}{x ^{4} + 1}

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

x \to 0 + lim ((1 + 4 x)^{\frac{5}{x}})

What is (\partial)/(\partial u)(u^2-v^2) ?
The answer to (\partial)/(\partial u)(u^2-v^2) is 2u