What is (\partial)/(\partial x)(e^{x^2+y^2+1}) ?

The answer to (\partial)/(\partial x)(e^{x^2+y^2+1}) is e^{x^2+y^2+1}*2x

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(\partial)/(\partial x)(e^{x^2+y^2+1})

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + 1})

e^{x^{2} + y^{2} + 1} \cdot 2 x

Solution steps

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + 1})

Treat

y

as a constant

Apply the chain rule:

e^{x^{2} + y^{2} + 1} \frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

= e^{x^{2} + y^{2} + 1} \frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 1) = 2 x

= e^{x^{2} + y^{2} + 1} \cdot 2 x

x \to \infty lim (\frac{1}{( 2 x + 1 ) ^{\frac{1}{x}}})

x \to \infty lim (x e)

\int e^{x} (sin (x)) d x

\frac{2}{s ( s ^{2} + 4 s )}

\int_{6}^{8} \frac{84}{( x - 6 ) ^{3}} d x

What is (\partial)/(\partial x)(e^{x^2+y^2+1}) ?
The answer to (\partial)/(\partial x)(e^{x^2+y^2+1}) is e^{x^2+y^2+1}*2x