What is the derivative of (40t^2)/(t^2+150) ?

The derivative of (40t^2)/(t^2+150) is (12000t)/((t^2+150)^2)

What is the first derivative of (40t^2)/(t^2+150) ?

The first derivative of (40t^2)/(t^2+150) is (12000t)/((t^2+150)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{40 t ^{2}}{t ^{2} + 150}

\frac{12000 t}{( t ^{2} + 150 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{40 t ^{2}}{t ^{2} + 150})

Take the constant out:

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

= 40 \frac{d}{d t} (\frac{t ^{2}}{t ^{2} + 150})

Apply the Quotient Rule:

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

= 40 \cdot \frac{\frac{d}{d t} ( t ^{2} ) ( t ^{2} + 150 ) - \frac{d}{d t} ( t ^{2} + 150 ) t ^{2}}{( t ^{2} + 150 ) ^{2}}

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

\frac{d}{d t} (t^{2} + 150) = 2 t

= 40 \cdot \frac{2 t ( t ^{2} + 150 ) - 2 t t ^{2}}{( t ^{2} + 150 ) ^{2}}

Simplify

40 \cdot \frac{2 t ( t ^{2} + 150 ) - 2 t t ^{2}}{( t ^{2} + 150 ) ^{2}} : \frac{12000 t}{( t ^{2} + 150 ) ^{2}}

= \frac{12000 t}{( t ^{2} + 150 ) ^{2}}

x \to 0 + lim (\frac{3}{x} - \frac{2}{ln ( x )})

\int \frac{- 1}{x ^{3}} d x

\int_{- 2}^{2} \frac{1}{x ^{2}} d x

\int 2 e^{x} + 2 x - 1 d x

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) d x + x^{3} y^{2} d y = 0

What is the derivative of (40t^2)/(t^2+150) ?
The derivative of (40t^2)/(t^2+150) is (12000t)/((t^2+150)^2)
What is the first derivative of (40t^2)/(t^2+150) ?
The first derivative of (40t^2)/(t^2+150) is (12000t)/((t^2+150)^2)