derivative y=3sin(x^3-5x^2+8x+0.5)

解答

导数

y = 3 sin (x^{3} - 5 x^{2} + 8 x + 0.5)

3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)

求解步骤

\frac{d}{d x} (3 sin (x^{3} - 5 x^{2} + 8 x + 0.5))

将常数提出:

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

= 3 \frac{d}{d x} (sin (x^{3} - 5 x^{2} + 8 x + 0.5))

使用连锁律:

cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

= cos (x^{3} - 5 x^{2} + 8 x + 0.5) \frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5)

\frac{d}{d x} (x^{3} - 5 x^{2} + 8 x + 0.5) = 3 x^{2} - 10 x + 8

= 3 cos (x^{3} - 5 x^{2} + 8 x + 0.5) (3 x^{2} - 10 x + 8)

\int 2 x (x^{2} + 1)^{- 4} d x

in v erse l a pl a ce \frac{7}{s ^{3} + 2 s ^{2} + 9 s + 18}

\int \frac{e ^{x}}{e ^{- 6 x}} d x

\frac{d}{d x} (\frac{5 x}{9 x ^{2} + 1})

y^{^{'}} = y - k