What is (\partial)/(\partial s)((t^2)/(s^3)) ?

The answer to (\partial)/(\partial s)((t^2)/(s^3)) is -(3t^2)/(s^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial s)((t^2)/(s^3))

\frac{\partial}{\partial s} (\frac{t ^{2}}{s ^{3}})

- \frac{3 t ^{2}}{s ^{4}}

Solution steps

\frac{\partial}{\partial s} (\frac{t ^{2}}{s ^{3}})

Treat

t

as a constant

Take the constant out:

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

= t^{2} \frac{\partial}{\partial s} (\frac{1}{s ^{3}})

Apply exponent rule:

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

= t^{2} \frac{\partial}{\partial s} (s^{- 3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= t^{2} (- 3 s^{- 3 - 1})

Simplify

t^{2} (- 3 s^{- 3 - 1}) : - \frac{3 t ^{2}}{s ^{4}}

= - \frac{3 t ^{2}}{s ^{4}}

What is (\partial)/(\partial s)((t^2)/(s^3)) ?
The answer to (\partial)/(\partial s)((t^2)/(s^3)) is -(3t^2)/(s^4)