en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2ln(x/4)

Solution

\frac{d}{d x} (x^{2} ln (\frac{x}{4}))

Solution

2 x ln (\frac{x}{4}) + x

Solution steps

\frac{d}{d x} (x^{2} ln (\frac{x}{4}))

Apply the Product Rule:

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

f = x^{2}, g = ln (\frac{x}{4})

= \frac{d}{d x} (x^{2}) ln (\frac{x}{4}) + \frac{d}{d x} (ln (\frac{x}{4})) x^{2}

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

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

= 2 x ln (\frac{x}{4}) + \frac{1}{x} x^{2}

\frac{1}{x} x^{2} = x

= 2 x ln (\frac{x}{4}) + x

Popular Examples

derivative of 6x^4(x^2-7x)

\frac{d}{d x} (6 x^{4} (x^{2} - 7 x))

integral from 0 to pi/2 of 17cos^5(x)

\int_{0}^{\frac{π}{2}} 17 cos^{5} (x) d x

integral of (2x)/(x^2-3x-10)

\int \frac{2 x}{x ^{2} - 3 x - 10} d x

(\partial)/(\partial y)(x^{1/2}*y^{1/2})

\frac{\partial}{\partial y} (x^{\frac{1}{2}} \cdot y^{\frac{1}{2}})

d/(dt)((cos(t))/(sin(t)))

\frac{d}{d t} (\frac{cos ( t )}{sin ( t )})

Frequently Asked Questions (FAQ)

What is the derivative of x^2ln(x/4) ?
The derivative of x^2ln(x/4) is 2xln(x/4)+x
What is the first derivative of x^2ln(x/4) ?
The first derivative of x^2ln(x/4) is 2xln(x/4)+x