What is the d/(dy)(e^{2x+y}) ?

The d/(dy)(e^{2x+y}) is e^{2x+y}

What is the first d/(dy)(e^{2x+y}) ?

The first d/(dy)(e^{2x+y}) is e^{2x+y}

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

e^{2 x + y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= e^{2 x + y}

f (x) = arctan (x)

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