derivative arctan(x^2+1)

解答

导数

arctan (x^{2} + 1)

\frac{2 x}{x ^{4} + 2 x ^{2} + 2}

求解步骤

\frac{d}{d x} (arctan (x^{2} + 1))

使用连锁律:

\frac{1}{( x ^{2} + 1 ) ^{2} + 1} \frac{d}{d x} (x^{2} + 1)

= \frac{1}{( x ^{2} + 1 ) ^{2} + 1} \frac{d}{d x} (x^{2} + 1)

\frac{d}{d x} (x^{2} + 1) = 2 x

= \frac{1}{( x ^{2} + 1 ) ^{2} + 1} \cdot 2 x

化简

\frac{1}{( x ^{2} + 1 ) ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

= \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

d er i v a t i v e y = \frac{( x - 3 ) ^{2} - 4}{x ^{2} + 2}

d er i v a t i v e \frac{x ^{2} - 5}{1 - 3 x ^{2}}

d er i v a t i v e \frac{2 x}{( x ^{2} + y ^{2} )}

d er i v a t i v e lo g_{10} (x^{6} + 5)

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