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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

y = 10 x, y = x^{2}

3 x^{2} + 24 x - y^{2} + 2 y = - 44

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

\int_{0}^{4} e^{x} d x

\int_{- 2}^{0} 1 + (- 4)^{2} d x

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