What is (\partial)/(\partial x)(1/2 (x^2+4y^2)) ?

The answer to (\partial)/(\partial x)(1/2 (x^2+4y^2)) is x

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(\partial)/(\partial x)(1/2 (x^2+4y^2))

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 4 y^{2}))

x

Solution steps

\frac{\partial}{\partial x} (\frac{1}{2} (x^{2} + 4 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} + 4 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} (4 y^{2}))

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

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

Simplify

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

= x

\frac{\partial}{\partial x} (\frac{1}{2 x})

2 x y \frac{d y}{d x} = y^{2} - x^{2} + 1

100 x^{2} + 400 x + 5000, 0.5

\int e^{y (1 - x)} d x

\frac{d}{d x} y = 7 x^{2} cos (x) cot (x)

What is (\partial)/(\partial x)(1/2 (x^2+4y^2)) ?
The answer to (\partial)/(\partial x)(1/2 (x^2+4y^2)) is x