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

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

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

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

e^{x^{2}} \cdot 2 x + 2 y

Solution steps

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

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

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

= e^{x^{2}} \cdot 2 x + 2 y

\int x^{\frac{1}{2}} ln (x) d x

\frac{d}{d x} (a + b x^{2})

x \to - 2 lim (g (x))

y = e^{- 0.6 x}, y = 1.4 x + 1, x = 0, x = 5

\frac{d}{d x} (in (x - 1))

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