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

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

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

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

2 y x

Solution steps

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

Treat

y, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= y (0 + 2 x + 0)

Simplify

= 2 y x

A (- 4, - \frac{3}{2}) y B (5, - 2)

\frac{( x ^{2} + 6 x + 6 )}{2 ( x ^{2} + 2 x + 2 )}

\frac{2 x ^{4} + a x ^{3} + ( 1 - a ) x ^{2} + a x + ( 3 - a )}{x - 1}

(\frac{10 + x}{x - 2}) (\frac{3}{10 - x})

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

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