en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 4x^2ln(4x)

Solution

derivative of

4 x^{2} ln (4 x)

Solution

4 (2 x ln (4 x) + x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

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

= 4 (2 x ln (4 x) + x)

Popular Examples

(\partial)/(\partial x)(-x^3y^2)

\frac{\partial}{\partial x} (- x^{3} y^{2})

integral of sin^3(20x)

\int sin^{3} (20 x) d x

limit as x approaches 0+of x^{14x}

x \to 0 + lim (x^{14 x})

d/(dt)(-12cos^2(t)sin(t))

\frac{d}{d t} (- 12 cos^{2} (t) sin (t))

derivative of 7x^5+(3cos(x)/x)

\frac{d}{d x} (7 x^{5} + \frac{3 cos ( x )}{x})

Frequently Asked Questions (FAQ)

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