What is the derivative of y= t/((t-5)^2) ?

The derivative of y= t/((t-5)^2) is (-5-t)/((t-5)^3)

What is the first derivative of y= t/((t-5)^2) ?

The first derivative of y= t/((t-5)^2) is (-5-t)/((t-5)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{t}{( t - 5 ) ^{2}}

\frac{- 5 - t}{( t - 5 ) ^{3}}

Solution steps

\frac{d}{d t} (\frac{t}{( t - 5 ) ^{2}})

Apply the Quotient Rule:

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

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

\frac{d t}{d t} = 1

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

= \frac{1 \cdot ( t - 5 ) ^{2} - 2 ( t - 5 ) t}{( ( t - 5 ) ^{2} ) ^{2}}

Simplify

\frac{1 \cdot ( t - 5 ) ^{2} - 2 ( t - 5 ) t}{( ( t - 5 ) ^{2} ) ^{2}} : \frac{- 5 - t}{( t - 5 ) ^{3}}

= \frac{- 5 - t}{( t - 5 ) ^{3}}

\int 5 cos^{3} (6 x) d x

\frac{\partial}{\partial x} (3 x^{3} + x^{2} y - 3 y^{3})

a x^{2}

\int 13 x^{2} sin (π x) d x

y = 10 x - x + 3, (100, 3)

What is the derivative of y= t/((t-5)^2) ?
The derivative of y= t/((t-5)^2) is (-5-t)/((t-5)^3)
What is the first derivative of y= t/((t-5)^2) ?
The first derivative of y= t/((t-5)^2) is (-5-t)/((t-5)^3)