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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

\int_{0}^{2} \frac{2}{8 - x ^{2}} d x

\frac{d}{d x} (cos (x) + 1)

\frac{d ^{2}}{d x ^{2}} (5 ln (x^{5}))

\int (\frac{2 x ^{3} + 5 x ^{2} - 2 x}{x}) d x

sin (x), cos (x) - 1

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