derivative of ln((tan(sqrt(x))^3))

解答

\frac{d}{d x} (ln ((tan (x))^{3}))

\frac{3 sec ^{2} ( x )}{2 x tan ( x )}

求解步骤

\frac{d}{d x} (ln ((tan (x))^{3}))

使用连锁律:

\frac{1}{( tan ( x ) ) ^{3}} \frac{d}{d x} ((tan (x))^{3})

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

\frac{d}{d x} ((tan (x))^{3}) = \frac{3 sec ^{2} ( x ) tan ^{2} ( x )}{2 x}

= \frac{1}{( tan ( x ) ) ^{3}} \cdot \frac{3 sec ^{2} ( x ) tan ^{2} ( x )}{2 x}

化简

\frac{1}{tan ^{3} ( x )} \cdot \frac{3 sec ^{2} ( x ) tan ^{2} ( x )}{2 x} : \frac{3 sec ^{2} ( x )}{2 x tan ( x )}

= \frac{3 sec ^{2} ( x )}{2 x tan ( x )}

\frac{d}{d x} (x^{2} - 5 x - 6)

\int \frac{1}{12} x d x

y^{^{'}} = x + 8 y

\frac{d y}{d t} - y = 1, y (0) = 1

\int \frac{1}{25 - 4 x ^{2}} d x