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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

t sin (0.89 t)

\frac{5}{8 t}

\frac{\partial}{\partial y} (x^{2} y^{3} z)

y = - 3 x + 5

k = 1 \sum \infty 3^{k} 7

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