What is the derivative of (55.9)/(t^2-0.31t+11.2) ?

The derivative of (55.9)/(t^2-0.31t+11.2) is -(55.9(2t-0.31))/((t^2-0.31t+11.2)^2)

What is the first derivative of (55.9)/(t^2-0.31t+11.2) ?

The first derivative of (55.9)/(t^2-0.31t+11.2) is -(55.9(2t-0.31))/((t^2-0.31t+11.2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{55.9}{t ^{2} - 0.31 t + 11.2}

- \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{55.9}{t ^{2} - 0.31 t + 11.2})

Take the constant out:

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

= 55.9 \frac{d}{d t} (\frac{1}{t ^{2} - 0.31 t + 11.2})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 55.9 \frac{d}{d t} ((t^{2} - 0.31 t + 11.2)^{- 1})

Apply the chain rule:

- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

= - \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

\frac{d}{d t} (t^{2} - 0.31 t + 11.2) = 2 t - 0.31

= 55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31))

Simplify

55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31)) : - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

= - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

What is the derivative of (55.9)/(t^2-0.31t+11.2) ?
The derivative of (55.9)/(t^2-0.31t+11.2) is -(55.9(2t-0.31))/((t^2-0.31t+11.2)^2)
What is the first derivative of (55.9)/(t^2-0.31t+11.2) ?
The first derivative of (55.9)/(t^2-0.31t+11.2) is -(55.9(2t-0.31))/((t^2-0.31t+11.2)^2)