What is (\partial)/(\partial y)(x^3e^{xy}) ?

The answer to (\partial)/(\partial y)(x^3e^{xy}) is e^{xy}x^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x^3e^{xy})

\frac{\partial}{\partial y} (x^{3} e^{x y})

e^{x y} x^{4}

Solution steps

\frac{\partial}{\partial y} (x^{3} e^{x y})

Treat

x

as a constant

Take the constant out:

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

= x^{3} \frac{\partial}{\partial y} (e^{x y})

Apply the chain rule:

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

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

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

= x^{3} e^{x y} x

Simplify

x^{3} e^{x y} x : e^{x y} x^{4}

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

x \to 0 lim (3 x^{2} - 5)

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

\frac{d y}{d t} = sin (t) - y

\int \frac{- 1}{1 + e ^{x}} d x

x \to - 5 lim (2 (- \frac{3}{10}) (x) - 3)

What is (\partial)/(\partial y)(x^3e^{xy}) ?
The answer to (\partial)/(\partial y)(x^3e^{xy}) is e^{xy}x^4