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

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

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(\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}}

\int 7 x^{4} - 6 x^{3} + 4 x^{2} + C d x

(2 x^{3} + 5)^{4}

\int (x^{2} + 5 x) cos (x) d x

\frac{d y}{d x} = 0.5 y

\frac{d}{d x} (\frac{8 x ^{2} - 40}{3 x ^{\frac{1}{3}}})

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