What is (\partial)/(\partial x)(4x(x^2+y^2)-4a^2x) ?

The answer to (\partial)/(\partial x)(4x(x^2+y^2)-4a^2x) is 4(3x^2+y^2)-4a^2

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(\partial)/(\partial x)(4x(x^2+y^2)-4a^2x)

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2}) - 4 a^{2} x)

4 (3 x^{2} + y^{2}) - 4 a^{2}

Solution steps

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2}) - 4 a^{2} x)

Treat

a, y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x (x^{2} + y^{2})) - \frac{\partial}{\partial x} (4 a^{2} x)

\frac{\partial}{\partial x} (4 x (x^{2} + y^{2})) = 4 (3 x^{2} + y^{2})

\frac{\partial}{\partial x} (4 a^{2} x) = 4 a^{2}

= 4 (3 x^{2} + y^{2}) - 4 a^{2}

\frac{a}{x}

\frac{s}{( s - 1 )}

y (1 + x^{2}) y^{^{'}} - x (6 + y^{2}) = 0

y = 5 x^{4} e^{x} + e^{x} x^{5}

x \to 1 lim (- 6 + 2 x^{2})

What is (\partial)/(\partial x)(4x(x^2+y^2)-4a^2x) ?
The answer to (\partial)/(\partial x)(4x(x^2+y^2)-4a^2x) is 4(3x^2+y^2)-4a^2