What is the derivative of m(t)=(4t+11)/(7t^2-3t+5) ?

The derivative of m(t)=(4t+11)/(7t^2-3t+5) is (-28t^2-154t+53)/((7t^2-3t+5)^2)

What is the first derivative of m(t)=(4t+11)/(7t^2-3t+5) ?

The first derivative of m(t)=(4t+11)/(7t^2-3t+5) is (-28t^2-154t+53)/((7t^2-3t+5)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

m (t) = \frac{4 t + 11}{7 t ^{2} - 3 t + 5}

\frac{- 28 t ^{2} - 154 t + 53}{( 7 t ^{2} - 3 t + 5 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{4 t + 11}{7 t ^{2} - 3 t + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 4 t + 11 ) ( 7 t ^{2} - 3 t + 5 ) - \frac{d}{d t} ( 7 t ^{2} - 3 t + 5 ) ( 4 t + 11 )}{( 7 t ^{2} - 3 t + 5 ) ^{2}}

\frac{d}{d t} (4 t + 11) = 4

\frac{d}{d t} (7 t^{2} - 3 t + 5) = 14 t - 3

= \frac{4 ( 7 t ^{2} - 3 t + 5 ) - ( 14 t - 3 ) ( 4 t + 11 )}{( 7 t ^{2} - 3 t + 5 ) ^{2}}

Expand

4 (7 t^{2} - 3 t + 5) - (14 t - 3) (4 t + 11) : - 28 t^{2} - 154 t + 53

= \frac{- 28 t ^{2} - 154 t + 53}{( 7 t ^{2} - 3 t + 5 ) ^{2}}

\frac{d}{d x} (\frac{x}{x + \frac{y}{x}})

\int cos^{8} (x) sin (x) d x

\int cos (5 t) d t

x \to 1 - lim (4 x)

y^{^{'}} = 0.05 ln (\frac{2000}{y}) y

What is the derivative of m(t)=(4t+11)/(7t^2-3t+5) ?
The derivative of m(t)=(4t+11)/(7t^2-3t+5) is (-28t^2-154t+53)/((7t^2-3t+5)^2)
What is the first derivative of m(t)=(4t+11)/(7t^2-3t+5) ?
The first derivative of m(t)=(4t+11)/(7t^2-3t+5) is (-28t^2-154t+53)/((7t^2-3t+5)^2)