What is (\partial)/(\partial x)(4x^3y^2+3) ?

The answer to (\partial)/(\partial x)(4x^3y^2+3) is 12x^2y^2

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(\partial)/(\partial x)(4x^3y^2+3)

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

12 x^{2} y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{3} y^{2}) = 12 y^{2} x^{2}

\frac{\partial}{\partial x} (3) = 0

= 12 y^{2} x^{2} + 0

Simplify

= 12 x^{2} y^{2}

y = ln (2 x + 1)

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

\int 4 x e^{9 x} d x

f (x) = x^{4} - 5 x^{2} - x, at x = 1

y = \frac{3}{x}, (5, \frac{3}{5})

What is (\partial)/(\partial x)(4x^3y^2+3) ?
The answer to (\partial)/(\partial x)(4x^3y^2+3) is 12x^2y^2