derivative of (sin^2(x)/(cos(x)))

解答

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

sin (x) (1 + sec^{2} (x))

求解步骤

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

化简

\frac{sin ^{2} ( x )}{cos ( x )} : sin (x) tan (x)

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

使用微分乘法定则:

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

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

= \frac{d}{d x} (sin (x)) tan (x) + \frac{d}{d x} (tan (x)) sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

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

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

化简

cos (x) tan (x) + sec^{2} (x) sin (x) : sin (x) (1 + sec^{2} (x))

= sin (x) (1 + sec^{2} (x))

a re a (- x + 2), (- x^{2} - 2 x), - 2, - 1

ma c l a u r in (1 + x)^{- \frac{2}{3}}

t an g e n t y = (1 + 2 x)^{10}, (0, 1)

d er i v a t i v e 5 x arcsin (x)

\int \frac{1 - 2 y}{y ^{2}} d y