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

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

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

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

\frac{x}{2}

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{x}{2} + 0

Simplify

= \frac{x}{2}

y = 1 x

\int_{3}^{\infty} e^{- 4 x} d x

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

\frac{3}{s + 1}

\int \frac{sec ^{6} ( x )}{tan ^{3} ( x )} d x

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