What is (\partial)/(\partial x)(x^3+3xy^2-15x-12y) ?

The answer to (\partial)/(\partial x)(x^3+3xy^2-15x-12y) is 3x^2+3y^2-15

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(\partial)/(\partial x)(x^3+3xy^2-15x-12y)

\frac{\partial}{\partial x} (x^{3} + 3 x y^{2} - 15 x - 12 y)

3 x^{2} + 3 y^{2} - 15

Solution steps

\frac{\partial}{\partial x} (x^{3} + 3 x y^{2} - 15 x - 12 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 y^{2}) - \frac{\partial}{\partial x} (15 x) - \frac{\partial}{\partial x} (12 y)

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

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

\frac{\partial}{\partial x} (15 x) = 15

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

= 3 x^{2} + 3 y^{2} - 15 - 0

Simplify

= 3 x^{2} + 3 y^{2} - 15

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} - 24 y = 0

x \to 0 - lim (x - 1)

\int_{0}^{1} 3 (x^{2} + 1) e^{- x} d x

x \to 3 + lim (7 x^{2} + 5)

x \to - 1 lim ([x])

What is (\partial)/(\partial x)(x^3+3xy^2-15x-12y) ?
The answer to (\partial)/(\partial x)(x^3+3xy^2-15x-12y) is 3x^2+3y^2-15