What is the d/(dt)({f}(t)(t)^{-1}) ?

The d/(dt)({f}(t)(t)^{-1}) is (d/(dt)({f}(t)))/t-({f}(t))/(t^2)

What is the first d/(dt)({f}(t)(t)^{-1}) ?

The first d/(dt)({f}(t)(t)^{-1}) is (d/(dt)({f}(t)))/t-({f}(t))/(t^2)

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\frac{d}{d t} (f (t) (t)^{- 1})

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

Solution steps

\frac{d}{d t} (f (t) (t)^{- 1})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (t), g = t^{- 1}

= \frac{d}{d t} (f (t)) t^{- 1} + \frac{d}{d t} (t^{- 1}) f (t)

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

= \frac{d}{d t} (f (t)) t^{- 1} + (- \frac{1}{t ^{2}}) f (t)

Simplify

\frac{d}{d t} (f (t)) t^{- 1} + (- \frac{1}{t ^{2}}) f (t) : \frac{\frac{d}{d t} ( f ( t ) )}{t} - \frac{f ( t )}{t ^{2}}

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

\int 18 cos (2 t) d t

\frac{d}{d t} (3 t - 1)

n = 1 \sum \infty n^{n} \cdot x^{n}

y^{^{''}} + 6 y^{^{'}} + 8 = 0

\frac{d y}{d x} = 2 x (x - 4)

What is the d/(dt)({f}(t)(t)^{-1}) ?
The d/(dt)({f}(t)(t)^{-1}) is (d/(dt)({f}(t)))/t-({f}(t))/(t^2)
What is the first d/(dt)({f}(t)(t)^{-1}) ?
The first d/(dt)({f}(t)(t)^{-1}) is (d/(dt)({f}(t)))/t-({f}(t))/(t^2)