What is the d/(dy)(2e^{xy^2}) ?

The d/(dy)(2e^{xy^2}) is 4e^{xy^2}xy

What is the first d/(dy)(2e^{xy^2}) ?

The first d/(dy)(2e^{xy^2}) is 4e^{xy^2}xy

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

4 e^{x y^{2}} x y

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= 4 e^{x y^{2}} x y

What is the d/(dy)(2e^{xy^2}) ?
The d/(dy)(2e^{xy^2}) is 4e^{xy^2}xy
What is the first d/(dy)(2e^{xy^2}) ?
The first d/(dy)(2e^{xy^2}) is 4e^{xy^2}xy