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

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

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

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

2 y

Solution steps

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

Simplify

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

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (1) = 0

= 0 + 2 y - 0

Simplify

= 2 y

g (x) = x^{2} + sin (x)

f (x) = (x - 3 x^{4}) tan (x)

\int 200 - 20 x - 3 x^{2} d x

\frac{d}{d x} (ln (x) \cdot e^{2 x})

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

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