en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(ln(4ye^{xy}))

Solution

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

Solution

y

Solution steps

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

Simplify

ln (4 y e^{x y}) : ln (4 y) + y x

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (ln (4 y)) = 0

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

= 0 + y

Simplify

= y

Popular Examples

limit as x approaches 3+of (x-3)/(x^2-9)

x \to 3 + lim (\frac{x - 3}{x ^{2} - 9})

derivative of 4x^3-5x^2+3x-5

\frac{d}{d x} (4 x^{3} - 5 x^{2} + 3 x - 5)

derivative of 4excos(x)derivative of

4 e x cos (x)

derivative of arctan(2x-1)

\frac{d}{d x} (arctan (2 x - 1))

x y^{^{'}} + 36 y = \frac{1}{x}

Frequently Asked Questions (FAQ)

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