derivative y=ln(5+2x+x^3)

解答

导数

y = ln (5 + 2 x + x^{3})

\frac{3 x ^{2} + 2}{5 + 2 x + x ^{3}}

求解步骤

\frac{d}{d x} (ln (5 + 2 x + x^{3}))

使用连锁律:

\frac{1}{5 + 2 x + x ^{3}} \frac{d}{d x} (5 + 2 x + x^{3})

= \frac{1}{5 + 2 x + x ^{3}} \frac{d}{d x} (5 + 2 x + x^{3})

\frac{d}{d x} (5 + 2 x + x^{3}) = 3 x^{2} + 2

= \frac{1}{5 + 2 x + x ^{3}} (3 x^{2} + 2)

化简

\frac{1}{5 + 2 x + x ^{3}} (3 x^{2} + 2) : \frac{3 x ^{2} + 2}{5 + 2 x + x ^{3}}

= \frac{3 x ^{2} + 2}{5 + 2 x + x ^{3}}

\int \frac{1}{cos ^{2} ( a y )} d y

\frac{\partial}{\partial x} (8 x^{2} + y^{2} - 9 y)

t an g e n t f (x) = x^{2} + 3 x + 1, at x = 4

x \to 0 lim (ln (0))

\int x^{3} (3 + x^{4})^{5} d x