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

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

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

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

- 2 e^{- y} x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 - 2 e^{- y} x

Simplify

= - 2 e^{- y} x

t^{3} e^{b \cdot t}

\frac{\partial}{\partial x} (ln (x + y^{4}))

x \to \infty lim (- \frac{x}{2})

x \to \frac{π}{2} lim (5 sin (x))

f (x) = - 9 x^{2}, at x = 2

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