What is the derivative of-(200ln(f/(40)))/(f+20) ?

The derivative of-(200ln(f/(40)))/(f+20) is -(200(f+20-fln(f/(40))))/(f(f+20)^2)

What is the first derivative of-(200ln(f/(40)))/(f+20) ?

The first derivative of-(200ln(f/(40)))/(f+20) is -(200(f+20-fln(f/(40))))/(f(f+20)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

- \frac{200 ln ( \frac{f}{40} )}{f + 20}

- \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

Solution steps

\frac{d}{df} - \frac{200 ln ( \frac{f}{40} )}{f + 20}

Take the constant out:

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

= - 200 \frac{d}{df} \frac{ln ( \frac{f}{40} )}{f + 20}

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 200 \cdot \frac{\frac{d}{df} ( ln ( \frac{f}{40} ) ) ( f + 20 ) - \frac{d}{df} ( f + 20 ) ln ( \frac{f}{40} )}{( f + 20 ) ^{2}}

\frac{d}{df} (ln (\frac{f}{40})) = \frac{1}{f}

\frac{d}{df} (f + 20) = 1

= - 200 \cdot \frac{\frac{1}{f} ( f + 20 ) - 1 \cdot ln ( \frac{f}{40} )}{( f + 20 ) ^{2}}

Simplify

- 200 \cdot \frac{\frac{1}{f} ( f + 20 ) - 1 \cdot ln ( \frac{f}{40} )}{( f + 20 ) ^{2}} : - \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

= - \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

What is the derivative of-(200ln(f/(40)))/(f+20) ?
The derivative of-(200ln(f/(40)))/(f+20) is -(200(f+20-fln(f/(40))))/(f(f+20)^2)
What is the first derivative of-(200ln(f/(40)))/(f+20) ?
The first derivative of-(200ln(f/(40)))/(f+20) is -(200(f+20-fln(f/(40))))/(f(f+20)^2)