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Popular >

(\partial)/(\partial s)(t/s)

Solution

\frac{\partial}{\partial s} (\frac{t}{s})

Solution

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

Solution steps

\frac{\partial}{\partial s} (\frac{t}{s})

Treat

t

as a constant

Take the constant out:

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

= t \frac{\partial}{\partial s} (\frac{1}{s})

Apply exponent rule:

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

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

Apply the Power Rule:

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

= t (- 1 \cdot s^{- 1 - 1})

Simplify

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

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

Popular Examples

integral from 0 to 1 of (x^3)/(x^2+1)

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 1} d x

integral of 1/5 x

\int \frac{1}{5} x d x

integral of 2/(x^3sqrt(x^4-81))

\int \frac{2}{x ^{3} x ^{4} - 81} d x

d/(dt)(e^{-at}cos(wt))

\frac{d}{d t} (e^{- a t} cos (wt))

integral of (x^22^x+x)/(x^2)

\int \frac{x ^{2} 2 ^{x} + x}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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