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

The answer to (\partial)/(\partial x)(4x^2-y^2+2y) is 8x

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

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

8 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

= 8 x - 0 + 0

Simplify

= 8 x

y = \frac{x}{3}, y = x - 2

\frac{d}{d x} (2 x^{2} + 4 x + 5)

e^{x + 3 y} d y = x d x

\int \frac{8}{x ^{2} + 1} d x

\int \frac{x ^{2}}{x ^{2} + 2 x + 2} d x

What is (\partial)/(\partial x)(4x^2-y^2+2y) ?
The answer to (\partial)/(\partial x)(4x^2-y^2+2y) is 8x