What is the derivative of t^{22}ln|t| ?

The derivative of t^{22}ln|t| is 22t^{21}ln|t|+t^{21}

What is the first derivative of t^{22}ln|t| ?

The first derivative of t^{22}ln|t| is 22t^{21}ln|t|+t^{21}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

t^{22} ln ∣ t ∣

22 t^{21} ln ∣ t ∣ + t^{21}

Solution steps

\frac{d}{d t} (t^{22} ln ∣ t ∣)

Apply the Product Rule:

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

f = t^{22}, g = ln ∣ t ∣

= \frac{d}{d t} (t^{22}) ln ∣ t ∣ + \frac{d}{d t} (ln ∣ t ∣) t^{22}

\frac{d}{d t} (t^{22}) = 22 t^{21}

\frac{d}{d t} (ln ∣ t ∣) = \frac{1}{t}

= 22 t^{21} ln ∣ t ∣ + \frac{1}{t} t^{22}

\frac{1}{t} t^{22} = t^{21}

= 22 t^{21} ln ∣ t ∣ + t^{21}

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

3 - x, 0

(2 x)^{^{'}}

\frac{d}{d x} (x^{2} - 25)

f (x) = x^{2} + 3 x, at x = 0

What is the derivative of t^{22}ln|t| ?
The derivative of t^{22}ln|t| is 22t^{21}ln|t|+t^{21}
What is the first derivative of t^{22}ln|t| ?
The first derivative of t^{22}ln|t| is 22t^{21}ln|t|+t^{21}