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

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

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

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

2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 2 x

Simplify

= 2 x

\frac{d}{d x} (f (x) (- x))

d er i v a t i v e 20 x^{\frac{7}{5}} - 6 x^{\frac{2}{13}}

t an g e n t x^{5}

\int csc^{2} (\frac{x}{3}) d x

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

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