What is (\partial)/(\partial x)(x^3+8x^2y+12y^2) ?

The answer to (\partial)/(\partial x)(x^3+8x^2y+12y^2) is 3x^2+16xy

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(\partial)/(\partial x)(x^3+8x^2y+12y^2)

\frac{\partial}{\partial x} (x^{3} + 8 x^{2} y + 12 y^{2})

3 x^{2} + 16 x y

Solution steps

\frac{\partial}{\partial x} (x^{3} + 8 x^{2} y + 12 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (8 x^{2} y) + \frac{\partial}{\partial x} (12 y^{2})

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

\frac{\partial}{\partial x} (8 x^{2} y) = 16 y x

\frac{\partial}{\partial x} (12 y^{2}) = 0

= 3 x^{2} + 16 y x + 0

Simplify

= 3 x^{2} + 16 x y

\frac{d y}{d x} + 8 y = e^{7 x}

\frac{d}{d x} (e^{x} (11 x^{2} - 22 x + 22))

\frac{d y}{d x}, y^{4} = 4 x y

x \to 0 lim (\frac{e ^{3 x} - 1}{2 x})

\frac{d}{d y} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}})

What is (\partial)/(\partial x)(x^3+8x^2y+12y^2) ?
The answer to (\partial)/(\partial x)(x^3+8x^2y+12y^2) is 3x^2+16xy