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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

y^{^{''}} - 9 y = 54

(- 8, - 6), (- 18, 6)

y = x^{2} - 3 x - 3, (2, - 5)

(- 5, - 11), (5, 3)

y^{^{'}} = y (2 - y)

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