What is the d/(dt)(1/(t^4)) ?

The d/(dt)(1/(t^4)) is -4/(t^5)

What is the first d/(dt)(1/(t^4)) ?

The first d/(dt)(1/(t^4)) is -4/(t^5)

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

- \frac{4}{t ^{5}}

Solution steps

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= - 4 t^{- 4 - 1}

Simplify

- 4 t^{- 4 - 1} : - \frac{4}{t ^{5}}

= - \frac{4}{t ^{5}}

- \frac{1}{x}

\int 8 x cos (5 x) d x

y^{^{''}} + 9 y^{^{'}} = 1

x \to - 2 lim (\frac{2 x}{x ^{2} - 4})

\int \frac{x ^{6} - x ^{3} + 25}{x ^{4} + 5 x ^{2}} d x