What is (\partial)/(\partial x)(e^{x^2+y^2+2y+5}) ?

The answer to (\partial)/(\partial x)(e^{x^2+y^2+2y+5}) is e^{x^2+y^2+2y+5}*2x

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(\partial)/(\partial x)(e^{x^2+y^2+2y+5})

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + 2 y + 5})

e^{x^{2} + y^{2} + 2 y + 5} \cdot 2 x

Solution steps

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + 2 y + 5})

Treat

y

as a constant

Apply the chain rule:

e^{x^{2} + y^{2} + 2 y + 5} \frac{\partial}{\partial x} (x^{2} + y^{2} + 2 y + 5)

= e^{x^{2} + y^{2} + 2 y + 5} \frac{\partial}{\partial x} (x^{2} + y^{2} + 2 y + 5)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 2 y + 5) = 2 x

= e^{x^{2} + y^{2} + 2 y + 5} \cdot 2 x

x \to 2 lim (\frac{- 2 x ^{2}}{x - 2})

\int (x - \frac{2}{x}) d x

x \to 0 lim (x^{2} - 8 x + 9)

e^{6}

\frac{d}{d z} (\frac{1}{z})

What is (\partial)/(\partial x)(e^{x^2+y^2+2y+5}) ?
The answer to (\partial)/(\partial x)(e^{x^2+y^2+2y+5}) is e^{x^2+y^2+2y+5}*2x