derivative of sec^5(x^7+4x^6)

解答

\frac{d}{d x} (sec^{5} (x^{7} + 4 x)^{6})

30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

求解步骤

\frac{d}{d x} ((sec^{5} (x^{7} + 4 x))^{6})

化简

(sec^{5} (x^{7} + 4 x))^{6} : sec^{30} (x^{7} + 4 x)

= \frac{d}{d x} (sec^{30} (x^{7} + 4 x))

使用连锁律:

30 (sec (x^{7} + 4 x))^{29} \frac{d}{d x} (sec (x^{7} + 4 x))

= 30 (sec (x^{7} + 4 x))^{29} \frac{d}{d x} (sec (x^{7} + 4 x))

\frac{d}{d x} (sec (x^{7} + 4 x)) = sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

= 30 (sec (x^{7} + 4 x))^{29} sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

化简

30 sec^{29} (x^{7} + 4 x) sec (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4) : 30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

= 30 sec^{30} (x^{7} + 4 x) tan (x^{7} + 4 x) (7 x^{6} + 4)

d er i v a t i v e x^{2020} + \frac{1}{3} x^{3} - 4 x^{2}

\frac{\partial}{\partial y} (x e^{2 x + 3 y})

\int (\frac{cos ( x )}{sin ^{2} ( x )}) d x

\int u d u

(ln^{3} (x))^{^{'}}