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

The answer to (\partial)/(\partial x)(x^3+3x^2y) is 3x^2+6yx

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

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

3 x^{2} + 6 y x

Solution steps

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

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} (3 x^{2} y)

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

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

= 3 x^{2} + 6 y x

x^{2} \frac{d y}{d x} = 4 x^{2} + 7 x y + 2 y^{2}

f (x) = x + 2, at x = 7

\int_{0}^{0.2} 600 x d x

- y^{^{''}} + 49 y = 0

\int sin^{2} (t) d t

What is (\partial)/(\partial x)(x^3+3x^2y) ?
The answer to (\partial)/(\partial x)(x^3+3x^2y) is 3x^2+6yx