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

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

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

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

2 e^{x^{2}} x

Solution steps

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

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 y^{3})

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

= e^{x^{2}} \cdot 2 x + 0

Simplify

= 2 e^{x^{2}} x

\int (x + 1) ln (x) d x

f (x) = x^{2} x^{3} + 1

\int x \cdot f (x) d x

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

\frac{\partial}{\partial y} (x^{3} - 6 x y + 8 y^{3})

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