derivative of 5sec(xtan(x))

解答

\frac{d}{d x} (5 sec (x) tan (x))

5 (- sec (x) + 2 sec^{3} (x))

求解步骤

\frac{d}{d x} (5 sec (x) tan (x))

将常数提出:

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

= 5 \frac{d}{d x} (sec (x) tan (x))

使用微分乘法定则:

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

f = sec (x), g = tan (x)

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

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

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

= 5 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

化简

5 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 5 (- sec (x) + 2 sec^{3} (x))

= 5 (- sec (x) + 2 sec^{3} (x))

\frac{\partial}{\partial x} (3 + 200 x^{2} + 300 y^{2})

t an g e n t f (x) = \frac{( 2 x - 1 )}{x + 3}, at x = 2

d er i v a t i v e f (x) = (2 x - 4)^{4} (x^{2} + x + 1)^{5}

\frac{\partial}{\partial x} (\frac{y}{2 - x})

d er i v a t i v e 5 \frac{1}{y ^{2}}