What is (\partial)/(\partial x)(4x^3y^2+1) ?

The answer to (\partial)/(\partial x)(4x^3y^2+1) is 12x^2y^2

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(\partial)/(\partial x)(4x^3y^2+1)

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 1)

12 x^{2} y^{2}

Solution steps

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 1)

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} (1)

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

\frac{\partial}{\partial x} (1) = 0

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

Simplify

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

y = \frac{( x ^{7} - 4 x ^{3} + 12 x )}{x ^{3}}

x \to 1 + lim (x^{\frac{9}{1 - x}})

2 sin (3 π x)

y^{^{'}} + \frac{2}{x} y = x, y (1) = 0

y = e^{x}

What is (\partial)/(\partial x)(4x^3y^2+1) ?
The answer to (\partial)/(\partial x)(4x^3y^2+1) is 12x^2y^2