en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 3xln(9x^2)

Solution

\frac{d}{d x} (3 x ln (9 x^{2}))

Solution

3 (2 ln (3 x) + 2)

Solution steps

\frac{d}{d x} (3 x ln (9 x^{2}))

Take the constant out:

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

= 3 \frac{d}{d x} (x ln (9 x^{2}))

Apply the Product Rule:

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

f = x, g = ln (9 x^{2})

= 3 (\frac{d x}{d x} ln (9 x^{2}) + \frac{d}{d x} (ln (9 x^{2})) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (ln (9 x^{2})) = \frac{2}{x}

= 3 (1 \cdot ln (9 x^{2}) + \frac{2}{x} x)

Simplify

3 (1 \cdot ln (9 x^{2}) + \frac{2}{x} x) : 3 (2 ln (3 x) + 2)

= 3 (2 ln (3 x) + 2)

Popular Examples

limit as x approaches 0 of e^{(1/x)}

x \to 0 lim (e^{(\frac{1}{x})})

integral of (1+(1/2)*2/((2*x+3)))

\int (1 + (\frac{1}{2}) \cdot \frac{2}{( 2 \cdot x + 3 )}) d x

derivative of (sin(x^2)/(sin^2(x)))

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

derivative of y=6x^2e^{-x}derivative of

y = 6 x^{2} e^{- x}

derivative of f(x)=2^{20}derivative of

f (x) = 2^{20}

Frequently Asked Questions (FAQ)

What is the derivative of 3xln(9x^2) ?
The derivative of 3xln(9x^2) is 3(2ln(3x)+2)
What is the first derivative of 3xln(9x^2) ?
The first derivative of 3xln(9x^2) is 3(2ln(3x)+2)