What is the derivative of xe^{y^2} ?

The derivative of xe^{y^2} is e^{y^2}+2e^{y^2}xy(dy)/(dx)

What is the first derivative of xe^{y^2} ?

The first derivative of xe^{y^2} is e^{y^2}+2e^{y^2}xy(dy)/(dx)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

\frac{d}{d x} (\frac{- x ^{2}}{2})

x \to \frac{c}{2 ^{+}} lim ([2 x - 4])

y^{^{''}} + y = 3

\int (sin (t)) d t

- 2 x^{3}

What is the derivative of xe^{y^2} ?
The derivative of xe^{y^2} is e^{y^2}+2e^{y^2}xy(dy)/(dx)
What is the first derivative of xe^{y^2} ?
The first derivative of xe^{y^2} is e^{y^2}+2e^{y^2}xy(dy)/(dx)