What is (\partial)/(\partial y)(10y^2e^{10xy}) ?

The answer to (\partial)/(\partial y)(10y^2e^{10xy}) is 10(2ye^{10xy}+e^{10xy}*10xy^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(10y^2e^{10xy})

\frac{\partial}{\partial y} (10 y^{2} e^{10 x y})

10 (2 y e^{10 x y} + e^{10 x y} \cdot 10 x y^{2})

Solution steps

\frac{\partial}{\partial y} (10 y^{2} e^{10 x y})

Treat

x

as a constant

Take the constant out:

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

= 10 \frac{\partial}{\partial y} (y^{2} e^{10 x y})

Apply the Product Rule:

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

f = y^{2}, g = e^{10 x y}

= 10 (\frac{\partial}{\partial y} (y^{2}) e^{10 x y} + \frac{\partial}{\partial y} (e^{10 x y}) y^{2})

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

\frac{\partial}{\partial y} (e^{10 x y}) = e^{10 x y} \cdot 10 x

= 10 (2 y e^{10 x y} + e^{10 x y} \cdot 10 x y^{2})

t \to 0 lim (\frac{tan ( 3 t )}{t})

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

n = 1 \sum \infty (100) (\frac{1}{2})^{n}

- 1, 8, 4 e^{- 2 x} - 5

19 e^{x^{2}}

What is (\partial)/(\partial y)(10y^2e^{10xy}) ?
The answer to (\partial)/(\partial y)(10y^2e^{10xy}) is 10(2ye^{10xy}+e^{10xy}*10xy^2)