derivative ln(x^3+5x+3)

解答

导数

ln (x^{3} + 5 x + 3)

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

x \to 1 lim (x sin (\frac{1}{x}))

t an g e n t y = x^{4} - 3 x^{2} + 2, (1, 0)

x \to 2 - lim (\frac{∣ x - x ∣}{x - 2})

\frac{d}{d x} (tan (3 x) s c^{3} x)

\int \frac{1}{x 1 - 4 x ^{2}} d x