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

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

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

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

3 x^{2} + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} + y^{2}

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

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

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

= 1 \cdot (x^{2} + y^{2}) + 2 xx

Simplify

1 \cdot (x^{2} + y^{2}) + 2 xx : 3 x^{2} + y^{2}

= 3 x^{2} + y^{2}

(x + 19 - 45) (x + 19 + 45)

\frac{d ^{2}}{d x ^{2}} ((f (x, z, y)) (z^{3} - 2 x z + y))

, (4 + 9 v) (4 - 9)

(x^{2} - 2) (x^{2} - 6 x + 5)

, 150 (2 s - 150) - (2 s - 150)^{2} + 300 s - 2 s^{2}

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