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

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

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

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

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

Solution steps

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

Treat

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 x)

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

\frac{\partial}{\partial x} (4 x) = 4

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

t \to 1 lim (sin (3 π t))

y = x^{2} - 7, (- 5, 18)

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

x^{2} sin (3 x)

2 x sin (y) d x + x^{2} cos (y) d y = 0

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