What is (\partial)/(\partial x)(8xe^{x^2}+y^2) ?

The answer to (\partial)/(\partial x)(8xe^{x^2}+y^2) is 8(2e^{x^2}x^2+e^{x^2})

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(\partial)/(\partial x)(8xe^{x^2}+y^2)

\frac{\partial}{\partial x} (8 x e^{x^{2}} + y^{2})

8 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{\partial}{\partial x} (8 x e^{x^{2}} + y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x e^{x^{2}}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (8 x e^{x^{2}}) = 8 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

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

= 8 (e^{x^{2}} + 2 e^{x^{2}} x^{2}) + 0

Simplify

= 8 (2 e^{x^{2}} x^{2} + e^{x^{2}})

\int \frac{x + 4}{x ^{2} + 4} d x

(x + 2)^{3}, 2 x^{2} - 8 x + 8, 0

x \to 1 lim (x + 4 - 12)

f (x) = x + 2, at x = 1

What is (\partial)/(\partial x)(8xe^{x^2}+y^2) ?
The answer to (\partial)/(\partial x)(8xe^{x^2}+y^2) is 8(2e^{x^2}x^2+e^{x^2})