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

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

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

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

2 φ x

Solution steps

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

Treat

φ, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= φ (2 x + 0)

Simplify

= 2 φ x

(x + e^{2 x} y)^{2}

\frac{( ( ( x ^{3} - 2 x ) ^{5} ) )}{5}

ln (x) (x + 3)

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

(x - 3) (x - 4 - 4 i) (x + 4 + 4 i)

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