What is (\partial)/(\partial x)(5y^3e^{x-2}-2xy) ?

The answer to (\partial)/(\partial x)(5y^3e^{x-2}-2xy) is 5y^3e^{x-2}-2y

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(\partial)/(\partial x)(5y^3e^{x-2}-2xy)

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2} - 2 x y)

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

Solution steps

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2} - 2 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 y^{3} e^{x - 2}) - \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (5 y^{3} e^{x - 2}) = 5 y^{3} e^{x - 2}

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

= 5 y^{3} e^{x - 2} - 2 y

\int (x e^{- x^{2}} + \frac{e ^{x}}{e ^{x} + 3}) d x

\int_{- 2}^{3} \frac{15}{x ^{4}} d x

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

x^{2} \frac{d y}{d x} = y - y x

\frac{\partial}{\partial y} (y cos (x y))

What is (\partial)/(\partial x)(5y^3e^{x-2}-2xy) ?
The answer to (\partial)/(\partial x)(5y^3e^{x-2}-2xy) is 5y^3e^{x-2}-2y