What is (\partial)/(\partial x)(4xln(x)y) ?

The answer to (\partial)/(\partial x)(4xln(x)y) is 4y(ln(x)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(4xln(x)y)

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

4 y (ln (x) + 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

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

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

= 4 y (1 \cdot ln (x) + \frac{1}{x} x)

Simplify

4 y (1 \cdot ln (x) + \frac{1}{x} x) : 4 y (ln (x) + 1)

= 4 y (ln (x) + 1)

\int (2 x + y)^{8} d x

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

\frac{d}{d s} (\frac{s}{s ^{2} + b ^{2}})

t e^{2 t}

y^{^{''}} + 5 y^{^{'}} + 4 y = sin (3 x)

What is (\partial)/(\partial x)(4xln(x)y) ?
The answer to (\partial)/(\partial x)(4xln(x)y) is 4y(ln(x)+1)