What is (\partial)/(\partial x)(7xe^{x^2}+y^2) ?

The answer to (\partial)/(\partial x)(7xe^{x^2}+y^2) is 7(2e^{x^2}x^2+e^{x^2})

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(\partial)/(\partial x)(7xe^{x^2}+y^2)

\frac{\partial}{\partial x} (7 x e^{x^{2}} + y^{2})

7 (2 e^{x^{2}} x^{2} + e^{x^{2}})

Solution steps

\frac{\partial}{\partial x} (7 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} (7 x e^{x^{2}}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (7 x e^{x^{2}}) = 7 (e^{x^{2}} + 2 e^{x^{2}} x^{2})

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

= 7 (e^{x^{2}} + 2 e^{x^{2}} x^{2}) + 0

Simplify

= 7 (2 e^{x^{2}} x^{2} + e^{x^{2}})

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(x^{2} + 2 y^{^{'}}) y^{^{''}} + 2 x y^{^{'}} = 0

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What is (\partial)/(\partial x)(7xe^{x^2}+y^2) ?
The answer to (\partial)/(\partial x)(7xe^{x^2}+y^2) is 7(2e^{x^2}x^2+e^{x^2})