What is (\partial)/(\partial x)(2x^2-y^2+3x-y) ?

The answer to (\partial)/(\partial x)(2x^2-y^2+3x-y) is 4x+3

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(\partial)/(\partial x)(2x^2-y^2+3x-y)

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

4 x + 3

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (3 x) = 3

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

= 4 x - 0 + 3 - 0

Simplify

= 4 x + 3

x \to + 0 lim (x^{2} + 1)

6 arcsin (e^{\frac{x}{2}})

\frac{d}{d x} (\frac{3 ^{x} + 8}{3 ^{x} - 1})

\int e^{- 0.25 x} d x

\int 2 x y^{2} d x

What is (\partial)/(\partial x)(2x^2-y^2+3x-y) ?
The answer to (\partial)/(\partial x)(2x^2-y^2+3x-y) is 4x+3