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

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

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(\partial)/(\partial x)(3xe^y-x^3-e^{3y})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (e^{3 y}) = 0

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

Simplify

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

\int 3 x^{2} y + e^{x} sin (y) d x

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

\frac{d}{d x} (x^{2} \cdot ln (2 x))

\frac{s}{s ^{2} + 25}

\int_{0}^{\frac{π}{3}} sin^{4} (3 x) d x

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