en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=t(ln(3t))^2

Solution

derivative of

y = t (ln (3 t))^{2}

Solution

ln^{2} (3 t) + 2 ln (3 t)

Solution steps

\frac{d}{d t} (t (ln (3 t))^{2})

Apply the Product Rule:

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

f = t, g = (ln (3 t))^{2}

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

\frac{d t}{d t} = 1

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

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

Simplify

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

= ln^{2} (3 t) + 2 ln (3 t)

Popular Examples

derivative of sqrt(x^3+2)

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

slope of 5/(sqrt(x))slope

\frac{5}{x}

integral of 10x^{3/2}

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

integral of (e^{-x}-e^2)*(e^x+e^{-5})

\int (e^{- x} - e^{2}) \cdot (e^{x} + e^{- 5}) d x

integral from 0 to 1 of 3^{-x}

\int_{0}^{1} 3^{- x} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=t(ln(3t))^2 ?
The derivative of y=t(ln(3t))^2 is ln^2(3t)+2ln(3t)
What is the first derivative of y=t(ln(3t))^2 ?
The first derivative of y=t(ln(3t))^2 is ln^2(3t)+2ln(3t)