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

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

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

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

2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 2 x + 0 - 0

Simplify

= 2 x

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

\frac{\partial}{\partial y} (x e^{3 y})

\frac{\partial}{\partial x} (\frac{4 x - 3 y}{4 x + 3 y})

f (x) = - 16 t^{2} - 8 t + 64

(x^{2} - 3) (x^{3} - 2 x)

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