What is (\partial)/(\partial x)(1/2 (x^2+10y^2)) ?

The answer to (\partial)/(\partial x)(1/2 (x^2+10y^2)) is x

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(\partial)/(\partial x)(1/2 (x^2+10y^2))

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

x

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 10 y^{2}))

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{2} \frac{\partial}{\partial x} (x^{2} + 10 y^{2})

Apply the Sum/Difference Rule:

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

= \frac{1}{2} (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (10 y^{2}))

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

\frac{\partial}{\partial x} (10 y^{2}) = 0

= \frac{1}{2} (2 x + 0)

Simplify

\frac{1}{2} (2 x + 0) : x

= x

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What is (\partial)/(\partial x)(1/2 (x^2+10y^2)) ?
The answer to (\partial)/(\partial x)(1/2 (x^2+10y^2)) is x