derivative of 2sec^2(x*tan(x))

解答

\frac{d}{d x} (2 sec^{2} (x) \cdot tan (x))

- 4 sec^{2} (x) + 6 sec^{4} (x)

求解步骤

\frac{d}{d x} (2 sec^{2} (x) tan (x))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (sec^{2} (x) tan (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec^{2} (x), g = tan (x)

= 2 (\frac{d}{d x} (sec^{2} (x)) tan (x) + \frac{d}{d x} (tan (x)) sec^{2} (x))

\frac{d}{d x} (sec^{2} (x)) = 2 sec^{2} (x) tan (x)

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= 2 (2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x))

化简

2 (2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x)) : - 4 sec^{2} (x) + 6 sec^{4} (x)

= - 4 sec^{2} (x) + 6 sec^{4} (x)

x d x + (x^{2} y + 4 y) d y = 0

y^{^{'}} + 5 y = 2

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

\frac{d}{d x} (A (e^{2 x} + 2 e^{2 x} x))

\frac{d}{d x} (- 2 cot (x) + 6 x^{4} csc (x))