derivative f(x)=sqrt(8-x^3)

解答

导数

f (x) = 8 - x^{3}

- \frac{3 x ^{2}}{2 8 - x ^{3}}

求解步骤

\frac{d}{d x} (8 - x^{3})

使用连锁律:

\frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

= \frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

\frac{d}{d x} (8 - x^{3}) = - 3 x^{2}

= \frac{1}{2 8 - x ^{3}} (- 3 x^{2})

化简

\frac{1}{2 8 - x ^{3}} (- 3 x^{2}) : - \frac{3 x ^{2}}{2 8 - x ^{3}}

= - \frac{3 x ^{2}}{2 8 - x ^{3}}

s l o p e x + y = 3

t an g e n t f (x) = 7 x^{2} + 2 x - 7, at x = - 3

s l o p e - 3 x + 5 y = 2 x + 3 y

c a r t es ian (4, - \frac{2 π}{3})

c a r t es ian (- 2, \frac{5 π}{4})