What is the derivative of (5t+300)/(t^2+25) ?

The derivative of (5t+300)/(t^2+25) is (-5t^2-600t+125)/((t^2+25)^2)

What is the first derivative of (5t+300)/(t^2+25) ?

The first derivative of (5t+300)/(t^2+25) is (-5t^2-600t+125)/((t^2+25)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{5 t + 300}{t ^{2} + 25}

\frac{- 5 t ^{2} - 600 t + 125}{( t ^{2} + 25 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{5 t + 300}{t ^{2} + 25})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 5 t + 300 ) ( t ^{2} + 25 ) - \frac{d}{d t} ( t ^{2} + 25 ) ( 5 t + 300 )}{( t ^{2} + 25 ) ^{2}}

\frac{d}{d t} (5 t + 300) = 5

\frac{d}{d t} (t^{2} + 25) = 2 t

= \frac{5 ( t ^{2} + 25 ) - 2 t ( 5 t + 300 )}{( t ^{2} + 25 ) ^{2}}

Expand

5 (t^{2} + 25) - 2 t (5 t + 300) : - 5 t^{2} - 600 t + 125

= \frac{- 5 t ^{2} - 600 t + 125}{( t ^{2} + 25 ) ^{2}}

\frac{d}{d x} (\frac{x - 2}{2 x + 1})

f (x) = 2 x - 5 x, (4, - 2)

h \to 0 lim (3 x^{2} + 2 x h + h^{2})

\int 20 x ln (x) d x

\int (x^{3} e^{4 x}) d x

What is the derivative of (5t+300)/(t^2+25) ?
The derivative of (5t+300)/(t^2+25) is (-5t^2-600t+125)/((t^2+25)^2)
What is the first derivative of (5t+300)/(t^2+25) ?
The first derivative of (5t+300)/(t^2+25) is (-5t^2-600t+125)/((t^2+25)^2)