derivative arctan(sqrt(5x^2-1))

解答

导数

arctan (5 x^{2} - 1)

\frac{1}{x 5 x ^{2} - 1}

求解步骤

\frac{d}{d x} (arctan (5 x^{2} - 1))

使用连锁律:

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

\frac{d}{d x} (5 x^{2} - 1) = \frac{5 x}{5 x ^{2} - 1}

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1}

化简

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1} : \frac{1}{x 5 x ^{2} - 1}

= \frac{1}{x 5 x ^{2} - 1}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = 1 + 9 x^{2}

\int 3 sec^{4} (x) d x

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d er i v a t i v e f (x) = 2 \cdot 7^{2 x^{2} + 3}