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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y^{2}}, g = x

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

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

\frac{\partial}{\partial x} (x) = 1

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

Simplify

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

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