derivative 9/(t^4)

解答

导数

\frac{9}{t ^{4}}

- \frac{36}{t ^{5}}

求解步骤

\frac{d}{d t} (\frac{9}{t ^{4}})

将常数提出:

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

= 9 \frac{d}{d t} (\frac{1}{t ^{4}})

使用指数法则:

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

= 9 \frac{d}{d t} (t^{- 4})

使用幂法则:

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

= 9 (- 4 t^{- 4 - 1})

化简

9 (- 4 t^{- 4 - 1}) : - \frac{36}{t ^{5}}

= - \frac{36}{t ^{5}}

\int \frac{2 x}{3 x ^{2} + 1} d x

\int_{- 5}^{5} (4 - ∣ x ∣) d x

d er i v a t i v e y = 8 csc (2 x^{4} - 7 x + 3)

\frac{d}{d x} (5 x^{5} f (x))

y^{^{'}} = e^{t + y}, y (0) = 0