derivative of asin^3(x/3)

解答

\frac{d}{d x} (a sin^{3} (\frac{x}{3}))

a sin^{2} (\frac{x}{3}) cos (\frac{x}{3})

求解步骤

\frac{d}{d x} (a sin^{3} (\frac{x}{3}))

将常数提出:

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

= a \frac{d}{d x} (sin^{3} (\frac{x}{3}))

使用连锁律:

3 (sin (\frac{x}{3}))^{2} \frac{d}{d x} (sin (\frac{x}{3}))

= 3 (sin (\frac{x}{3}))^{2} \frac{d}{d x} (sin (\frac{x}{3}))

\frac{d}{d x} (sin (\frac{x}{3})) = cos (\frac{x}{3}) \frac{1}{3}

= a \cdot 3 (sin (\frac{x}{3}))^{2} cos (\frac{x}{3}) \frac{1}{3}

化简

a \cdot 3 sin^{2} (\frac{x}{3}) cos (\frac{x}{3}) \frac{1}{3} : a sin^{2} (\frac{x}{3}) cos (\frac{x}{3})

= a sin^{2} (\frac{x}{3}) cos (\frac{x}{3})

y^{^{'}} + \frac{y}{x} = \frac{e ^{x}}{x}

t an g e n t 5 x + 4, at x = 9

x \to - 2 lim (4 x^{2} - 3)

f (x) = 2 - x^{2}

x \to 1 lim (f (x) (x^{2} - 2 x))