What is the first d/(dt)(4/t) ?

The first d/(dt)(4/t) is -4/(t^2)

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d/(dt)(4/t)

\frac{d}{d t} (\frac{4}{t})

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

Solution steps

\frac{d}{d t} (\frac{4}{t})

Take the constant out:

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

= 4 \frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

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

= 4 \frac{d}{d t} (t^{- 1})

Apply the Power Rule:

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

= 4 (- 1 \cdot t^{- 1 - 1})

Simplify

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

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

x \to + 0 lim ((e^{2 x} + x)^{\frac{1}{x}})

\int csc^{2} (3 x) cos (3 x) d x

x \to 0 lim (x - 2)

y^{^{''}} - 6 y^{^{'}} - 2 y + 1 = cos (2 x)

(x^{2} + 4) \frac{d y}{d x} + 3 x y = x