derivative tan^{-2}(x)

解答

导数

tan^{- 2} (x)

- 2 cot^{3} (x) sec^{2} (x)

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

= - 2 cot^{3} (x) sec^{2} (x)

\frac{d}{d a} (\frac{( a - t ^{2} )}{( b \cdot x )})

d er i v a t i v e - 12 x

d er i v a t i v e (x^{2} - x)^{3}

\frac{d}{d h} (0.606 \cdot h^{3} + 0.27 \cdot h^{2} + 0.12 \cdot h)

d er i v a t i v e (2 x^{2} - 4 x + 1) (6 x - 5)