What is (\partial)/(\partial x)(e^{4xy}*4y) ?

The answer to (\partial)/(\partial x)(e^{4xy}*4y) is 16e^{4xy}y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{4xy}*4y)

\frac{\partial}{\partial x} (e^{4 x y} \cdot 4 y)

16 e^{4 x y} y^{2}

Solution steps

\frac{\partial}{\partial x} (e^{4 x y} \cdot 4 y)

Treat

y

as a constant

Take the constant out:

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

= 4 y \frac{\partial}{\partial x} (e^{4 x y})

Apply the chain rule:

e^{4 x y} \frac{\partial}{\partial x} (4 x y)

= e^{4 x y} \frac{\partial}{\partial x} (4 x y)

\frac{\partial}{\partial x} (4 x y) = 4 y

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

Simplify

4 y e^{4 x y} \cdot 4 y : 16 e^{4 x y} y^{2}

= 16 e^{4 x y} y^{2}

x^{2} y^{^{'}} + 2 x y = 5 y^{3}

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0

y^{^{'}} = \frac{( x ^{2} + y )}{x + 1}

y^{^{'}} + \frac{y}{x} = x^{- 4}

s (t) = 14 + 15 sin (14 π t)

What is (\partial)/(\partial x)(e^{4xy}*4y) ?
The answer to (\partial)/(\partial x)(e^{4xy}*4y) is 16e^{4xy}y^2