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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (\frac{sin ( x )}{1 + tan ( x )})

x + \frac{3}{x}, at x = 2

f (x) = 4 - 2 x

x \to 2 lim (\frac{( x ^{6} - 64 )}{x - 2})

f (x) = 2 x

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