derivative y=sec(sqrt(3x^4+5))

解答

导数

y = sec (3 x^{4} + 5)

\frac{6 x ^{3} sec ( 3 x ^{4} + 5 ) tan ( 3 x ^{4} + 5 )}{3 x ^{4} + 5}

求解步骤

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

使用连锁律:

sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{d}{d x} (3 x^{4} + 5)

= sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{d}{d x} (3 x^{4} + 5)

\frac{d}{d x} (3 x^{4} + 5) = \frac{6 x ^{3}}{3 x ^{4} + 5}

= sec (3 x^{4} + 5) tan (3 x^{4} + 5) \frac{6 x ^{3}}{3 x ^{4} + 5}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 x ^{3} sec ( 3 x ^{4} + 5 ) tan ( 3 x ^{4} + 5 )}{3 x ^{4} + 5}

θ \to 0 lim (\frac{cos ( θ ) - 1}{θ})

\int_{0}^{2} π (\frac{1}{x + 4})^{2} d x

d er i v a t i v e f (x) = ln (81 sin^{2} (x))

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

x \to 3 lim (\frac{x - 3}{x - 2})