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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\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}

Vereinfache

\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}

\int x^{3} x^{2} + 9 d x

\frac{\partial}{\partial x} (sin (π (6 x - y)))

d er i v a t i v e arctan (\frac{1 + t}{1 - t})

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

\int \frac{3}{60 - t} d t