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

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

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

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

2 x + y^{2}

Solution steps

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

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

= 2 x + 0 + y^{2} + 0

Simplify

= 2 x + y^{2}

f (t) = 3 sin (2 t)

\int x^{2} - 5 x + 6 d x

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{3}{4}})

cos (a^{5} + x^{5})

\int \frac{x}{x ^{2} + 16} d x

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