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

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

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

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

e^{2 x + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= e^{2 x + y}

\frac{d}{d θ} (θ cos (θ) sin (θ))

\int \frac{cos ( θ )}{5 + 4 cos ( θ )} d θ

\frac{d}{d y} (3 x^{2} y + e^{y})

\frac{3 x}{4}

\frac{\partial}{\partial x} ((4 x^{4} y^{2} + 9) 2)

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