derivative of sec(x-1/(x^3)+5)

解答

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

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

求解步骤

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

\frac{d}{d x} (5) = 0

= sec (x) tan (x) - (- \frac{3}{x ^{4}}) + 0

化简

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

x \to 0 lim (x ln (tan (2 x)))

8 y^{^{''}} - 8 y^{^{'}} + 4 y = 0

\frac{d y}{d x} = 9 - \frac{3 y}{250}

d er i v a t i v e Y (x) = e^{4 x + 3}

\frac{d}{d y} (y^{2} - 1)