What is (\partial)/(\partial x)(x^3e^{x^2+y}-12y^2) ?

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

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(\partial)/(\partial x)(x^3e^{x^2+y}-12y^2)

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

2 e^{x^{2} + y} x^{4} + 3 e^{x^{2} + y} x^{2}

Solution steps

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

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

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

= 3 e^{x^{2} + y} x^{2} + 2 e^{x^{2} + y} x^{4} - 0

Simplify

= 2 e^{x^{2} + y} x^{4} + 3 e^{x^{2} + y} x^{2}

y = - 2 x sin (x^{2})

\frac{s - 3}{s ^{2} - 3 s + 2}

x \to 10 lim (\frac{10 x}{2 x + 5})

\int - 45 t^{\frac{2}{3}} - 80 d t

\int_{0}^{\infty} 2 x e^{- 2 x} d x

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